CN108320628A - The study mold of square body side surface displaypattern and its 90 ° of rotation process methods - Google Patents
The study mold of square body side surface displaypattern and its 90 ° of rotation process methods Download PDFInfo
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- CN108320628A CN108320628A CN201810105649.8A CN201810105649A CN108320628A CN 108320628 A CN108320628 A CN 108320628A CN 201810105649 A CN201810105649 A CN 201810105649A CN 108320628 A CN108320628 A CN 108320628A
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- G09B23/00—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes
- G09B23/02—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for mathematics
- G09B23/04—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for mathematics for geometry, trigonometry, projection or perspective
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Abstract
The study mold of square body side surface displaypattern and its 90 ° of rotation process methods, it is related to a kind of study mold and its operating method.In junior middle school's study stage, since figure is a variety of after cube expansion, student is needed to memorize mechanically one by one, student is difficult to differentiate whether the displaypattern being made of six panels is square body side surface displaypattern.The first composition panel, the second composition panel, third composition panel and the 4th composition panel enclose square frame in the present invention, 5th composition panel is located at the top of square frame, 6th composition panel is arranged in the bottom end of square frame, and six composition panels are detachably connected;Method is one, two, three or four composition panel rotational structure as a whole will to be selected in the displaypattern of six composition panels formation in the present invention, and residue composition panel is as fixed structure;Judge that unitary rotation structure whether there is 90 ° of angles with fixed structure, existing can be rotated by 90 °.The present invention is used for aided education or study.
Description
Technical field
The present invention relates to a kind of study mold and its operating methods, belong to instructional technology field.
Background technology
Currently, for Junior, about the relevant knowledge of square body side surface displaypattern, existing teaching method is past
Toward all listing all displaypatterns one by one, student is allowed to memorize mechanically, also some utilizes pithy formula, not only to remember pithy formula in this way,
It is also understood that pithy formula, it will also be toward covering in pithy formula when use, utilization is very dumb, not only time-consuming also to take mental, and is easy to
Error.
Invention content
The object of the present invention is to provide a kind of study mold of square body side surface displaypattern and its 90 ° of rotation process sides
Method, since figure is a variety of after cube expansion, needs student to memorize mechanically one by one, student to solve in junior middle school's study stage
It is difficult to that the problem of whether displaypattern of six panels composition is cube expansion figure differentiated.
The present invention adopts the technical scheme that solve above-mentioned technical problem:
A kind of study mold of pros' body side surface displaypattern, it includes the first composition panel, the second composition panel, third
Form panel, the 4th composition panel, the 5th composition panel and the 6th composition panel, the first composition panel, the second composition panel, the
Three composition panels, the 4th composition panel, the 5th composition panel and the 6th composition panel are rectangular plate body, the first composition panel,
Second composition panel, third composition panel and the 4th composition panel are enclosed square frame, the 5th composition panel successively
Be arranged on the top of square frame, the edge of the 5th composition panel respectively with the first composition panel, the second composition panel, the
Three composition panels and the 4th composition panel are detachably connected, and the 6th composition panel is arranged in the bottom end of square frame, and the 5th
The edge for forming panel forms panel with the first composition panel, the second composition panel, third composition panel and the 4th respectively
It is detachably connected;
The edge of the first composition panel forms face with the second composition panel, the 6th composition panel, the 4th respectively
Plate and the 5th composition panel are detachably connected;
The edge of the second composition panel forms face with the first composition panel, the 5th composition panel, third respectively
Plate and the 6th composition panel are detachably connected;
The edge of the third composition panel forms face with the second composition panel, the 6th composition panel, the 4th respectively
Plate and the 5th composition panel are detachably connected;
The edge of the 4th composition panel forms face with third composition panel, the 6th composition panel, first respectively
Plate and the 5th composition panel are detachably connected.
A kind of study mold of pros' body side surface displaypattern, preferably, when the first composition panel, the second composition
It is square that panel, third composition panel, the 4th composition panel, the 5th composition panel and the 6th composition panel are in same plane composition
When basic figure is unfolded in body side surface, the first composition panel, the second composition panel, third composition panel and the 4th composition panel are successively
Arrangement form stripe board, the 5th composition panel and the 6th composition panel are separately positioned on the both sides of the first composition panel.
A kind of study mold of pros' body side surface displaypattern, preferably, the edge of the first composition panel
Place is respectively arranged with the first magnetic stripe, the second magnetic stripe, third magnetic stripe and the 4th magnetic stripe, and the second composition panel is close to the first composition
One end of panel is provided with the 5th magnetic stripe, and the second composition panel is magnetic by the first magnetic stripe of the 5th magnetic stripe and the first composition panel
Connection;The 6th composition panel is provided with the 6th magnetic stripe close to one end of the first composition panel, and the 6th composition panel passes through the
Six magnetic stripes are connect with the second magnetic stripe magnetism of the first composition panel;The 4th composition panel is close to one end of the first composition panel
It is provided with the 7th magnetic stripe, the 4th composition panel is connect by the 7th magnetic stripe with the third magnetic stripe magnetism of the first composition panel;It is described
5th composition panel is provided with the 8th magnetic stripe close to one end of the first composition panel, and the 5th composition panel passes through the 8th magnetic stripe and the
The 4th magnetic stripe magnetism connection of one composition panel.
A kind of study mold of pros' body side surface displaypattern, preferably, the left upper end angle of the first composition panel,
Head rod, the second connecting rod, third connecting rod and the 4th are respectively arranged at upper right side angle, lower-left end angle and bottom righthand side angle
Connecting rod is respectively arranged with the first connected ball, the second connected ball, third connected ball and the at the first end of composition four of panel angle
Four connected balls, head rod are correspondingly arranged with the first connected ball, and the second connecting rod is correspondingly arranged with the second connected ball, and third connects
Extension bar is correspondingly arranged with third connected ball, and the 4th connecting rod is correspondingly arranged with the 4th connected ball;
One end of head rod is hinged with the first composition panel, the other end of head rod and the first connected ball
Outer wall is slidably matched, and the second composition panel is mutually cut with scissors close to the end angle of the first connected ball by the first connected ball and the first composition panel
It connects, the 5th composition panel is hinged close to the end angle of the first connected ball by the first connected ball and the first composition panel;
One end of second connecting rod is hinged with the first composition panel, the other end of the second connecting rod and the second connected ball
Outer wall is slidably matched, and the 5th composition panel is mutually cut with scissors close to the end angle of the second connected ball by the second connected ball and the first composition panel
It connects, the 4th composition panel is hinged close to the end angle of the second connected ball by the second connected ball and the first composition panel;
One end of third connecting rod is hinged with the first composition panel, the other end and the third connected ball of third connecting rod
Outer wall is slidably matched, and the second composition panel is mutually cut with scissors close to the end angle of third connected ball by third connected ball and the first composition panel
It connects, the 6th composition panel is hinged close to the end angle of third connected ball by third connected ball and the first composition panel;
One end of 4th connecting rod is hinged with the first composition panel, the other end of the 4th connecting rod and the 4th connected ball
Outer wall is slidably matched, and the 4th composition panel is mutually cut with scissors close to the end angle of the 4th connected ball by the 4th connected ball and the first composition panel
It connects, the 6th composition panel is hinged close to the end angle of the 4th connected ball by the 4th connected ball and the first composition panel.
A kind of study mold of pros' body side surface displaypattern, preferably, the second composition panel connects close to first
The end angle received is provided with forms panel close to the end of the first connected ball with matched 5th connecting rod of the first connected ball, the 5th
Angle be provided with matched 6th connecting rod of the first connected ball, be machined on the outer wall of the first connected ball with head rod,
5th connecting rod and the 6th matched chute system of connecting rod, chute system include the first pit, second dimple, N item annulars
Sliding slot and 2N transition pit are machined with the first pit and second dimple on the outer wall of first connected ball respectively, and first is recessed
Hole and second dimple are on the same diameter line of the first connected ball, and 2N transition pit is distributed on the first pit and second dimple
Between, every annular groove is connected with the first pit and second dimple respectively, and every annular groove is correspondingly arranged there are two mistake
Pit is crossed, two corresponding transition pits of every annular groove are connected.
A kind of study mold of pros' body side surface displaypattern, preferably, head rod, the 5th connecting rod and
The structure of 6th connecting rod is identical, one end of head rod the first connected ball of direction, the 5th connecting rod the first connected ball of direction
One end and one end of the 6th connecting rod towards the first connected ball match to be formed and matched with the first pit or second dimple
Connector.
90 ° of rotation process that the study mold of square body side surface displaypattern according to specific implementation mode six is realized
Method, this method include:
By first form panel, second composition panel, third composition panel, the 4th composition panel, the 5th composition panel and
6th composition panel is unfolded to form displaypattern in same plane successively;
Selected first composition panel, the second composition panel, third composition panel, the 4th composition panel, the 5th composition panel
Rotational structure, residue form panel conduct as a whole with one, two, three or four composition panel in the 6th composition panel
Fixed structure;
Judge to whether there is 90 ° of angles between unitary rotation structure and fixed structure;
When, there are when 90 ° of angles, when unitary rotation structure is rotated, entirety turns between unitary rotation structure and fixed structure
Dynamic structure and a connection edge of fixed structure separate, after being rotated by 90 °, another company of unitary rotation structure and fixed structure
Edge fit edge is fitted and connected, that is, forms a kind of square body side surface displaypattern.
90 ° of rotation process methods are further defined to:When unitary rotation structure is the first composition panel, judge
When being formed with 90 ° of angles between the left side of the first composition panel and other composition panels, the rotation direction of the first composition panel is
It rotates counterclockwise, rotational angle is 90 °;Judge to be formed with 90 ° between the right side of the first composition panel and other composition panels
When angle, the rotation direction of the first composition panel is to rotate clockwise, and rotational angle is 90 °.
90 ° of rotation process methods are further defined to:When unitary rotation structure includes two composition panels, two
It is disposed adjacent between composition panel;When unitary rotation structure includes three composition panels, phase successively between three composition panels
Neighbour is arranged;When unitary rotation structure includes four composition panels, arranged adjacent is arranged successively between four composition panels.
The invention has the advantages that:
1, the present invention is a kind of assisted learning mold of cube expansion figure and its 90 ° of rotation process methods of realization.
Structure of the invention design is simple and connection relation is stablized, and operating method is simple, flexible and effective, the first composition panel, second group
It can be suitable at cooperating between panel, third composition panel, the 4th composition panel, the 5th composition panel and the 6th composition panel
Profit is unfolded and converts various ways, the square body side surface displaypattern to be variously formulated, and helps to assist student more
The characteristics of remembering flexibly and easily and grasp square body side surface displaypattern and rule.Student can be rapid and accurate in the future for auxiliary
Really pick out whether the figure formed between six composition panels is cube expansion figure.
2, the study mould structure design in the present invention is simple, and manufacturing cost is cheap and easy realization, difficulty of processing are low.
3, the operating method in the present invention is flexible and changeable, and student can be assisted quickly to grasp square body side surface displaypattern
The characteristics of.
4, the present invention can also make demonstration teaching aid or toy, be used according to self-demand for academics and students.
Description of the drawings
Fig. 1 is the first dimensional structure diagram of the present invention;
Fig. 2 is the main structure diagram of the first composition panel 1;
Fig. 3 is the enlarged drawing at M in Fig. 2;
Fig. 4 is the dimensional structure diagram of the first connected ball 16;
Fig. 5 is the main structure diagram of the first connected ball 16;
Fig. 6 is that the stereochemical structure of connection relation between head rod 12, the 5th connecting rod 21 and the 6th connecting rod 22 is shown
It is intended to;
Fig. 7 is the dimensional structure diagram of head rod 12;
Fig. 8 is the main structure diagram of square body side surface expansion basic figure;
Fig. 9-1 is that the first composition panel 1, second forms panel 2, third composition panel the 3, the 4th forms panel 4, the 5th group
The first main structure diagram of mutual cooperation I-IV-I type figure of composition between panel 6 is formed at panel 5 and the 6th;
Fig. 9-2 is that the first composition panel 1, second forms panel 2, third composition panel the 3, the 4th forms panel 4, the 5th group
The second main structure diagram of mutual cooperation I-IV-I type figure of composition between panel 6 is formed at panel 5 and the 6th;
Fig. 9-3 is that the first composition panel 1, second forms panel 2, third composition panel the 3, the 4th forms panel 4, the 5th group
The third main structure diagram of mutual cooperation I-IV-I type figure of composition between panel 6 is formed at panel 5 and the 6th;
Fig. 9-4 is that the first composition panel 1, second forms panel 2, third composition panel the 3, the 4th forms panel 4, the 5th group
The 4th main structure diagram of mutual cooperation I-IV-I type figure of composition between panel 6 is formed at panel 5 and the 6th;
Fig. 9-5 is that the first composition panel 1, second forms panel 2, third composition panel the 3, the 4th forms panel 4, the 5th group
The 5th main structure diagram of mutual cooperation I-IV-I type figure of composition between panel 6 is formed at panel 5 and the 6th;
Fig. 9-6 is that the first composition panel 1, second forms panel 2, third composition panel the 3, the 4th forms panel 4, the 5th group
The 6th main structure diagram of mutual cooperation I-IV-I type figure of composition between panel 6 is formed at panel 5 and the 6th;
Fig. 9-7 is that the first composition panel 1, second forms panel 2, third composition panel the 3, the 4th forms panel 4, the 5th group
The 7th main structure diagram of mutual cooperation I-IV-I type figure of composition between panel 6 is formed at panel 5 and the 6th;
Fig. 9-8 is that the first composition panel 1, second forms panel 2, third composition panel the 3, the 4th forms panel 4, the 5th group
The 8th main structure diagram of mutual cooperation I-IV-I type figure of composition between panel 6 is formed at panel 5 and the 6th;
Fig. 9-9 is that the first composition panel 1, second forms panel 2, third composition panel the 3, the 4th forms panel 4, the 5th group
The 9th main structure diagram of mutual cooperation I-IV-I type figure of composition between panel 6 is formed at panel 5 and the 6th;
Fig. 9-10 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the tenth main structure diagram that panel 5 and the 6th forms mutual cooperation I-IV-I type figure of composition between panel 6;
Fig. 9-11 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the 11st main structure diagram that panel 5 and the 6th forms mutual cooperation I-IV-I type figure of composition between panel 6;
Fig. 9-12 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the 12nd main structure diagram that panel 5 and the 6th forms mutual cooperation I-IV-I type figure of composition between panel 6;
Fig. 9-13 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the 13rd main structure diagram that panel 5 and the 6th forms mutual cooperation I-IV-I type figure of composition between panel 6;
Fig. 9-14 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the 14th main structure diagram that panel 5 and the 6th forms mutual cooperation I-IV-I type figure of composition between panel 6;
Fig. 9-15 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the 15th main structure diagram that panel 5 and the 6th forms mutual cooperation I-IV-I type figure of composition between panel 6;
Figure 10-1 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the first main structure diagram that panel 5 and the 6th forms mutual cooperation II-III-I type figure of composition between panel 6;
Figure 10-2 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the second main structure diagram that panel 5 and the 6th forms mutual cooperation II-III-I type figure of composition between panel 6;
Figure 10-3 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the third main structure diagram that panel 5 and the 6th forms mutual cooperation II-III-I type figure of composition between panel 6;
Figure 10-4 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the 4th main structure diagram that panel 5 and the 6th forms mutual cooperation II-III-I type figure of composition between panel 6;
Figure 10-5 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the 5th main structure diagram that panel 5 and the 6th forms mutual cooperation II-III-I type figure of composition between panel 6;
Figure 10-6 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the 6th main structure diagram that panel 5 and the 6th forms mutual cooperation II-III-I type figure of composition between panel 6;
Figure 11-1 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the first main structure diagram that panel 5 and the 6th forms mutual cooperation I-III-II type figure of composition between panel 6;
Figure 11-2 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the second main structure diagram that panel 5 and the 6th forms mutual cooperation I-III-II type figure of composition between panel 6;
Figure 11-3 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the third main structure diagram that panel 5 and the 6th forms mutual cooperation I-III-II type figure of composition between panel 6;
Figure 11-4 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the 4th main structure diagram that panel 5 and the 6th forms mutual cooperation I-III-II type figure of composition between panel 6;
Figure 11-5 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the 5th main structure diagram that panel 5 and the 6th forms mutual cooperation I-III-II type figure of composition between panel 6;
Figure 11-6 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the 6th main structure diagram that panel 5 and the 6th forms mutual cooperation I-III-II type figure of composition between panel 6;
Figure 12-1 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the first main structure diagram that panel 5 and the 6th forms mutual cooperation II-II-II type figure of composition between panel 6;
Figure 12-2 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the second main structure diagram that panel 5 and the 6th forms mutual cooperation II-II-II type figure of composition between panel 6;
Figure 13-1 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the first main structure diagram that panel 5 and the 6th forms mutual cooperation III-III type figure of composition between panel 6;
Figure 13-2 is the first composition panel 1, second composition panel 2, the third composition composition panel the 4, the 5th of panel the 3, the 4th
Form the second main structure diagram that panel 5 and the 6th forms mutual cooperation III-III type figure of composition between panel 6;
Figure 14 is the second dimensional structure diagram of the present invention;
Figure 15 is the first deployed configuration schematic diagram based on Figure 14, shown in figure the position of the angle in 90 ° of shape at two with
And the rotation direction of each 90 ° of angles;
Figure 16 is second obtained after being rotated by 90 ° counterclockwise as rotation center using C points based on composition panel ABCD in Figure 15
Deployed configuration schematic diagram shows the position of the angle in 90 ° of shape at three and the rotation direction of each 90 ° of angles in figure.
Specific implementation mode
Specific implementation mode one:Illustrate that present embodiment, present embodiment include the first composition panel in conjunction with Fig. 1 to Figure 16
1, the second composition panel 2, the third composition composition composition composition panel 6 of panel 5 and the 6th of panel the 4, the 5th of panel the 3, the 4th, first
Form the composition of panel 1, second panel 2, third composition panel the 3, the 4th forms the composition panel 5 and the 6th of panel the 4, the 5th and forms face
Plate 6 is rectangular plate body, and the first composition panel 1, second forms panel 2, third composition panel 3 and the 4th forms panel 4 successively
It is enclosed square frame, the 5th composition panel 5 is arranged on the top of square frame, the surrounding of the 5th composition panel 5
Edge forms panel 2 with the first composition panel 1, second respectively, third composition panel 3 and the 4th forms panel 4 and is detachably connected, institute
It states the 6th composition panel 6 to be arranged in the bottom end of square frame, the edge of the 5th composition panel 5 forms panel with first respectively
1, the second composition panel 2, third composition panel 3 and the 4th form panel 4 and are detachably connected;
The edge of the first composition panel 1 forms panel the 6, the 4th with the second composition panel the 2, the 6th respectively and forms
Panel 4 and the 5th forms panel 5 and is detachably connected;
The edge of the second composition panel 2 forms panel 5, third composition with the first composition panel the 1, the 5th respectively
Panel 3 and the 6th forms panel 6 and is detachably connected;
The edge of the third composition panel 3 forms panel the 6, the 4th with the second composition panel the 2, the 6th respectively and forms
Panel 4 and the 5th forms panel 5 and is detachably connected;
The edge of the 4th composition panel 4 forms panel 6, first with third composition panel the 3, the 6th respectively and forms
Panel 1 and the 5th forms panel 5 and is detachably connected.
Specific implementation mode two:Illustrate present embodiment in conjunction with Fig. 8, Fig. 9-1 to Figure 13-2, forms panel 1, the when first
Two composition panels 2, third composition panel the 3, the 4th form the composition composition panel 6 of panel 5 and the 6th of panel the 4, the 5th and are in same
Plane form basic figure when, first composition panel 1, second form panel 2, third composition panel 3 and the 4th form panel 4 according to
Secondary arrangement form strip board, the 5th composition panel 5 and the 6th form the both sides that panel 6 is separately positioned on the first composition panel 1.
Basic figure is the basis of other square body side surface expanded views, the structure of basic figure and each composition panel it
Between installation position and connection relation be the optimum structure obtained by multiple sampling test.
Specific implementation mode three:Illustrate present embodiment, the edge of the first composition panel 1 in conjunction with Fig. 1 to Figure 16
It is respectively arranged with the first magnetic stripe 7-1, the second magnetic stripe 7-2, third magnetic stripe 7-3 and the 4th magnetic stripe 7-4, the second composition panel 2
One end of first composition panel 1 is provided with the 5th magnetic stripe 8-1, the second composition panel 2 passes through the 5th magnetic stripe 8-1 and first group
It is connected at the first magnetic stripe 7-1 magnetism of panel 1;The 6th composition panel 6 is provided with the close to one end of the first composition panel 1
Six magnetic stripes, the 6th composition panel 6 are connect by the 6th magnetic stripe with the second magnetic stripe 7-2 magnetism of the first composition panel 1;Described 4th
Composition panel 4 is provided with the 7th magnetic stripe close to one end of the first composition panel 1, and the 4th composition panel 4 passes through the 7th magnetic stripe and the
The third magnetic stripe 7-3 magnetism connection of one composition panel 1;The 5th composition panel 5 is arranged close to one end of the first composition panel 1
There are the 8th magnetic stripe 11-1, the 5th composition panel 5 magnetic by the 4th magnetic stripe 7-4 of the composition panels 1 of the 8th magnetic stripe 11-1 and first
Connection.
Magnetic connection type is stable and reliable in present embodiment, can realize the effect dismantled and connected in real time in real time,
Flexibility is strong, and transformation is fast, is convenient for teaching demonstration and voluntarily learning manipulation.
Specific implementation mode four:Illustrate present embodiment, left upper end angle, the right side of the first composition panel 1 in conjunction with Fig. 1 to Fig. 8
Head rod 12, the second connecting rod 13,14 and of third connecting rod are respectively arranged at upper corners, lower-left end angle and bottom righthand side angle
4th connecting rod 15 is respectively arranged with the first connected ball 16, the second connected ball 17, the at first end of composition four of panel 1 angle
Three connected balls 18 and the 4th connected ball 19, head rod 12 are correspondingly arranged with the first connected ball 16, the second connecting rod 13 and
Two connected balls 17 are correspondingly arranged, and third connecting rod 14 is correspondingly arranged with third connected ball 18, and the 4th connecting rod 15 is connect with the 4th
Ball 19 is correspondingly arranged;
One end of head rod 12 is hinged with the first composition panel 1, and the other end of head rod 12 and first connects
16 outer wall of receiving is slidably matched, and the second composition panel 2 passes through the first connected ball 16 and the close to the end angle of the first connected ball 16
One composition panel 1 is hinged, and the 5th composition panel 5 passes through the first connected ball 16 and first group close to the end angle of the first connected ball 16
It is hinged at panel 1;
One end of second connecting rod 13 is hinged with the first composition panel 1, and the other end of the second connecting rod 13 and second connects
17 outer wall of receiving is slidably matched, and the 5th composition panel 5 passes through the second connected ball 17 and the close to the end angle of the second connected ball 17
One composition panel 1 is hinged, and the 4th composition panel 4 passes through the second connected ball 17 and first group close to the end angle of the second connected ball 17
It is hinged at panel 1;
One end of third connecting rod 14 is hinged with the first composition panel 1, and the other end and the third of third connecting rod 14 connect
18 outer wall of receiving is slidably matched, and the second composition panel 2 passes through third connected ball 18 and the close to the end angle of third connected ball 18
One composition panel 1 is hinged, and the 6th composition panel 6 passes through third connected ball 18 and first group close to the end angle of third connected ball 18
It is hinged at panel 1;
One end of 4th connecting rod 15 is hinged with the first composition panel 1, and the other end of the 4th connecting rod 15 and the 4th connects
19 outer wall of receiving is slidably matched, and the 4th composition panel 4 passes through the 4th connected ball 19 and the close to the end angle of the 4th connected ball 19
One composition panel 1 is hinged, and the 6th composition panel 6 passes through the 4th connected ball 19 and first group close to the end angle of the 4th connected ball 19
It is hinged at panel 1.
The second composition panel 2, third composition panel the 3, the 4th form panel the 4, the 5th and form 5 and of panel in present embodiment
The connection relation and above-mentioned connection relation of 6th composition panel 6 are similarly.Other unmentioned structures and connection relation and specific reality
It is identical to apply mode one, two or three.
Specific implementation mode five:Present embodiment is further limiting for specific implementation mode four, and the second composition panel 2 leans on
The end angle of nearly first connected ball 16 is provided with to be leaned on 16 matched 5th connecting rod 21 of the first connected ball, the 5th composition panel 5
The end angle of nearly first connected ball 16 be provided with 16 matched 6th connecting rod 22 of the first connected ball, the first connected ball 16 it is outer
It is machined on wall and 22 matched chute system of head rod 12, the 5th connecting rod 21 and the 6th connecting rod, chute system
Including the first pit 20-1, second dimple 20-2, two annular groove 20-3 and four transition pit 20-4, first connection
It is machined with respectively on the outer wall of ball 16 at first pit 20-1 and second dimple 20-2, the first pit 20-1 and second dimple 20-2
In on the same diameter line of the first connected ball 16, four transition pit 20-4 are distributed on the first pit 20-1 and second dimple 20-2
Between, every annular groove 20-3 is connected with the first pit 20-1 and second dimple 20-2 respectively, every annular groove 20-3
Two transition pit 20-4, every annular groove 20-3 corresponding transition pit 20-4 are connected there are two being correspondingly arranged.
The structure of second connected ball 17, the structure of third connected ball 18, the structure of the 4th connected ball 19 and the first connected ball
16 structure is identical, and the setting of 16 sliding way system of the first connected ball can realize its own and the first 1, second group of panel of composition
The smooth sliding effect of panel 5 is formed at panel 2 and the 5th, sliding type is a variety of and rotation process is smooth, the first composition of cooperation
Panel 1, second forms head rod 12, the 5th connecting rod 21 and the 6th connecting rod 22 on the composition panel 5 of panel 2 and the 5th
Realize a variety of move modes, the first pit 20-1, second dimple 20-2, N annular groove 20-3 and 2N transition pit 20-4
Installation position and connection relation in the first connected ball 16 are to be able to ensure head rod 12, the 5th connecting rod 21
Or the 6th connecting rod 22 rotate 90 ° action it is accurate.It is similarly former in other composition panels and the matched work of connected ball
Reason.Chute system provides accurate movable passageway for each connecting rod.
It is connected by a link slot 20-5 between 2N transition pit 20-4, to be effectively increased 2N transition pit
Flexibility between 20-4.
Specific implementation mode six:Present embodiment is that specific implementation mode five further limits, head rod 12, the
Five connecting rods 21 are identical with the structure of the 6th connecting rod 22, and head rod 12 connects towards one end of the first connected ball 16, the 5th
One end of extension bar 21 towards one end of the first connected ball 16 and the 6th connecting rod 22 towards the first connected ball 16, which matches, to be formed
With the first pit 20-1 or the matched connectors of second dimple 20-2.Head rod 12, the connection of the 5th connecting rod 21 and the 6th
The structure setting of bar 22 be in order to coordinate the shape of the first pit 20-1 or second dimple 20-2, be four connection relations it is stable and
Rotation process is flexible, and the bottom of the first pit 20-1 is provided with the first magnetic piece 23, and the bottom of second dimple 20-2 is provided with
Two magnetic pieces, head rod 12 is towards one end of the first connected ball 16, the 5th connecting rod 21 towards the one of the first connected ball 16
End and one end of the 6th connecting rod 22 towards the first connected ball 16 are respectively arranged with and the first magnetic piece 23 or the second magnetic piece
The third magnetic piece 24 of magnetism connection, third magnetic piece 24 are arc-shaped connection sheet, and radian is 120 degree of circular arc degrees.First magnetic
Property piece 23 be circular piece, the side of head rod 12 towards the 5th connecting rod 21 is provided with the 4th magnetic piece 25, the 5th connection
The side of bar 21 towards head rod 12 be provided with 25 matched 5th magnetic piece 26 of the 4th magnetic piece, each transition is recessed
It is provided with the 6th magnetic piece 27 in the 20-4 of hole, similarly in the connection relation of other connecting rods.First magnetic piece 23 or the 6th is magnetic
Piece 27 and third magnetic piece 24, the 4th magnetic piece 25, the 5th magnetic piece 26 matches can realize head rod 12 and the 5th
It is stably connected between connecting rod 21 and easy-to-dismount effect, 12 length of of length no more than head rod of the 4th magnetic piece 25
One third, the similarly setting length in the 5th magnetic piece 26 in the 5th connecting rod 21, so as to be convenient for the first connection
It bar 12 and 21 fast quick-detach of the 5th connecting rod and is quickly adjacent to, does not influence the deformation velocity of entirety of the invention.Similarly connect in other
Connection relation between extension bar.
The shape of the first magnetic piece 23 is matched with the shape of the first pit 20-1 in present embodiment, the first magnetic piece 23
Top surface and the slot bottom of annular groove 20-3 be flush, the shape of the 6th magnetic piece 27 and the shape of transition pit 20-4 match
It closes, the top surface of the 6th magnetic piece 27 and the slot bottom of annular groove 20-3 are flush.Such setting can ensure each connecting rod side
Just dismounting and quickly and swimmingly move.
Specific implementation mode seven:Embodiment is described with reference to Fig. 1, and present embodiment includes:
First composition panel 1, second is formed into panel 2, third composition panel the 3, the 4th forms panel the 4, the 5th and forms face
Plate 5 and the 6th, which forms panel 6, to be unfolded successively in same plane;
Selected first composition panel 1, second forms panel 2, third composition panel the 3, the 4th forms panel the 4, the 5th and forms
One, two, three or four forms panel rotational structure as a whole, remaining composition face in the composition panel 6 of panel 5 and the 6th
Plate is as fixed structure;When selected first composition, 1 rotational structure as a whole of panel, the second composition panel 2, third form face
Plate the 3, the 4th forms panel the 4, the 5th and forms the composition panel 6 of panel 5 and the 6th as fixed structure, when selected first composition panel
1 and second composition panel 2 as a whole rotational structure when, third form panel the 3, the 4th form panel the 4, the 5th form panel 5
It is used as fixed structure with the 6th composition panel 6;The building form of other composition panels is similarly;
Judge to whether there is 90 ° of angles between unitary rotation structure and fixed structure;
When, there are when 90 ° of angles, when unitary rotation structure is rotated, entirety turns between unitary rotation structure and fixed structure
Dynamic structure and a connection edge of fixed structure separate, after being rotated by 90 °, another company of unitary rotation structure and fixed structure
Edge fit edge is fitted and connected, that is, forms a kind of square body side surface displaypattern.
When there are when non-90 degree angle, then the unitary rotation structure cannot rotate between unitary rotation structure and fixed structure.
Judge that the process between unitary rotation structure and fixed structure with the presence or absence of 90 ° of angles is exactly observation chart in this method
Whether it is formed with right angle at shape outer rim.
Obtained according to multiple sampling test, the present invention in study mold can quickly auxiliary judgment unitary rotation structure with
Whether can be rotated by 90 ° between fixed structure, when study mold switchs to flat deployable structure from stereochemical structure, when in the present invention
Annular groove 20-3 in first connected ball 16 is two, and the number of link slot 20-5 is one, the number of transition pit 20-4
Two annular groove 20-3, which are met at the first pit 20-1, when being four, in the first connected ball 16 is formed with four channels, when
When study mold is stereochemical structure, three connecting rods are in same first pit 20-1, when three connecting rods are respectively along respective
Corresponding channel becomes flat deployable structure when being moved to transition pit 20-4, at this time remaining channel position and direction
It can be as rotated by 90 ° location, be when if only there are one connecting rods or two connecting rods in the transition pit of connected ball
It is not revolvable.So as to assist teacher or student to carry out the quick decision process of direction of rotation.
Specific implementation mode eight:Illustrate that present embodiment, present embodiment are specific implementation mode in conjunction with Fig. 9-1 to 9-15
Seven further limit, when the left side of the 6th composition panel 6 is formed with 90 ° of angles with other composition panels, the 6th composition face
The direction of rotation of plate 6 is clockwise, and rotation angle is 90 °;When the right side of the 6th composition panel 6 and other composition panels are formed with
When 90 ° of angles, the direction of rotation of the 6th composition panel 6 is counterclockwise, and rotation angle is 90 °.Similarly in first form panel 1,
Second composition panel 2, third composition panel the 3, the 4th form the Principle of Rotating that panel 4 and the 5th forms panel 5.
Specific implementation mode nine:Present embodiment is that specific implementation mode seven or eight further limit, and works as unitary rotation
When structure includes two composition panels, it is disposed adjacent between two composition panels;When unitary rotation structure includes three composition faces
When plate, arranged adjacent is arranged successively between three composition panels;When unitary rotation structure includes four composition panels, four groups
At arranged adjacent is arranged successively between panel.
Specific implementation mode ten:Illustrate that present embodiment, Figure 14 are the stereograms of a square in conjunction with Figure 14 to Figure 16,
Stereogram is made of six square-shaped planars, 12 crest lines and eight vertex, and eight vertex have been marked out on the square
Title be respectively A, B, C, D, E, F, G, H, after stereogram side is unfolded, obtain the first unfolding assumption diagram in Figure 15, scheme
In show the position of the angle in 90 ° of shape at two and the direction of rotation of each 90 ° of angles,
Figure is shown from Figure 15 it can be seen that being vertical 90 ° by two crest lines that same crest line is divided into, when by two
When vertical crest line is merged into one, the crest line of adjacent side must be separated into two, that is, quite be that a square is flat
Face is rotated by 90 ° along the vertex with 90 ° of angles, it is assumed that by plane ABCD along C points be rotated by 90 ° counterclockwise to get to
The displaypattern of Figure 16, that is to say, that as long as it can be rotated in the plane at 90 ° of angles in square body side surface displaypattern, also
It is 90 ° of rotary process, mustn't thus wants any other memory.This learning method can not only increase students ' interest of study, and
And student thought can be opened up, be conducive to carry out innovative education, to asking square or the cuboid surface shortest distance below
Habit is also helpful, is also very beneficial to the culture of student's spatial thought.
Specific implementation mode 11:Between each face of the side expanded view of square it is connected with each other by crest line;Just
The angle of rotation in 90 ° of rotary process of side expanded view of cube must be 90 ° of angles;The side expanded view of square uses 90 °
When rotary process, as soon as when two crest lines are merged into crest line, another adjacent crest line is separated into two crest lines, and can only
It is that a crest line separates;When the side expanded view of square uses 90 ° of rotary process, rotation can be a face can also be more
A face rotates together with, and multiple faces here can be two, three, four or five;This method is to the similar expansion such as cuboid
Figure is also suitable.
Illustrate following embodiment in conjunction with beneficial effects of the present invention:
Embodiment one:The 5th composition panel 5 and the 6th in the basic figure of Fig. 8 is formed into panel 6 and presses 90 ° of difference to the right
Rotation combination successively, you can obtain 15 kinds of figures of I-IV-I type in Fig. 9-1 to Fig. 9-15.
Embodiment two:The 4th composition panel 4 for the first of Fig. 9-5 being formed panel 1 or Fig. 9-10 revolves up or down by 90 °
Turn, the rotation position of panel 6 is formed in conjunction with the 5th composition panel 5 or the 6th, you can obtain the II-III-I of Figure 10-1 to 10-6
Six kinds of figures of six kinds of figures of type and I-III-II type of Figure 11-1 to 11-6.
Embodiment three:The 4th composition panel 4 in Figure 10-2 is rotated down by 90 ° and forms panel with the 4th of Figure 11-5
4 rotate up by 90 °, you can obtain two kinds of figures of II-II-II type of Figure 12-1 and Figure 12-2.
Example IV:5th composition panel 5, first in Fig. 8 is formed the composition panel 6 of panel 1 and the 6th as a whole to turn
Dynamic structure can be obtained two kinds of figures of III-III type in Figure 13-1 and Figure 13-2 by 90 ° of rotations upward or downward.
Embodiment five:Judge whether when being the side displaypattern of square, as long as being obtained just by 90 ° of rotary process rotational energies
The structure of basic figure is unfolded in cube side, is not otherwise just.
Embodiment six:It when whether judge at 2 points or 3 points be same point, and rotates by 90 ° of rotary process, can overlap just
It is same point, is not otherwise just.
Claims (9)
1. a kind of study mold of pros' body side surface displaypattern, it is characterised in that:It includes the first composition panel (1), second
Panel (2), third composition panel (3), the 4th composition panel (4), the 5th composition panel (5) and the 6th composition panel (6) are formed,
First composition panel (1), the second composition panel (2), third composition panel (3), the 4th composition panel (4), the 5th composition panel
(5) and the 6th composition panel (6) is rectangular plate body, and the first composition panel (1), the second composition panel (2), third form panel
(3) and the 4th composition panel (4) is enclosed square frame successively, and the 5th composition panel (5) is arranged in square frame
The edge on top, the 5th composition panel (5) is formed with the first composition panel (1), the second composition panel (2), third respectively
Panel (3) and the 4th composition panel (4) are detachably connected, and the 6th composition panel (6) is arranged in the bottom end of square frame, the
The edge of five composition panels (5) forms panel (3) with the first composition panel (1), the second composition panel (2), third respectively
It is detachably connected with the 4th composition panel (4);
It is described first composition panel (1) edge respectively with second composition panel (2), the 6th composition panel (6), the 4th group
It is detachably connected at panel (4) and the 5th composition panel (5);
The edge of the second composition panel (2) forms panel (5), third group with the first composition panel (1), the 5th respectively
It is detachably connected at panel (3) and the 6th composition panel (6);
The edge of third composition panel (3) respectively with the second composition panel (2), the 6th composition panel (6), the 4th group
It is detachably connected at panel (4) and the 5th composition panel (5);
It is described 4th composition panel (4) edge respectively with third composition panel (3), the 6th composition panel (6), first group
It is detachably connected at panel (1) and the 5th composition panel (5).
2. the study mold of pros' body side surface displaypattern according to claim 1, it is characterised in that:When the first composition face
Plate (1), the second composition panel (2), third composition panel (3), the 4th composition panel (4), the 5th composition panel (5) and the 6th group
When being in same plane composition pros body side surface expansion basic figure at panel (6), the first composition panel (1), the second composition face
Plate (2), third composition panel (3) and the 4th composition panel (4) are arranged in order to form stripe board, and the 5th forms panel (5) and the
Six composition panels (6) are separately positioned on the both sides of the first composition panel (1).
3. the study mold of pros' body side surface displaypattern according to claim 1, it is characterised in that:First composition panel
(1) edge is respectively arranged with the first magnetic stripe (7-1), the second magnetic stripe (7-2), third magnetic stripe (7-3) and the 4th magnetic stripe
(7-4), the second composition panel (2) are provided with the 5th magnetic stripe (8-1) close to one end of the first composition panel (1), second group
It is connect with the first magnetic stripe (7-1) magnetism of the first composition panel (1) by the 5th magnetic stripe (8-1) at panel (2);Described 6th group
One end of the first composition panel (1) is provided with the 6th magnetic stripe at panel (6), the 6th composition panel (6) passes through the 6th magnetic stripe
It is connect with the second magnetic stripe (7-2) magnetism of the first composition panel (1);The 4th composition panel (4) is close to the first composition panel
(1) one end is provided with the 7th magnetic stripe, the third magnetic that the 4th composition panel (4) passes through the 7th magnetic stripe and the first composition panel (1)
The magnetic connection of item (7-3);The 5th composition panel (5) is provided with the 8th magnetic stripe close to one end of the first composition panel (1)
(11-1), the 5th composition panel (5) are magnetic by the 4th magnetic stripe (7-4) of the 8th magnetic stripe (11-1) and the first composition panel (1)
Connection.
4. the study mold of pros' body side surface displaypattern according to any one of claim 1 to 3, it is characterised in that:
The left upper end angle of first composition panel (1), upper right side angle are respectively arranged with head rod at lower-left end angle and bottom righthand side angle
(12), the second connecting rod (13), third connecting rod (14) and the 4th connecting rod (15), four ends angle of the first composition panel (1)
Place is respectively arranged with the first connected ball (16), the second connected ball (17), third connected ball (18) and the 4th connected ball (19), and first
Connecting rod (12) is correspondingly arranged with the first connected ball (16), and the second connecting rod (13) is correspondingly arranged with the second connected ball (17), the
Three connecting rods (14) are correspondingly arranged with third connected ball (18), and the 4th connecting rod (15) is correspondingly arranged with the 4th connected ball (19);
One end of head rod (12) is hinged with the first composition panel (1), the other end and first of head rod (12)
The outer wall of connected ball (16) is slidably matched, and the second composition panel (2) passes through the first connection close to the end angle of the first connected ball (16)
Ball (16) is hinged with the first composition panel (1), and the 5th composition panel (5) passes through first close to the end angle of the first connected ball (16)
Connected ball (16) is hinged with the first composition panel (1);
One end of second connecting rod (13) is hinged with the first composition panel (1), the other end and second of the second connecting rod (13)
The outer wall of connected ball (17) is slidably matched, and the 5th composition panel (5) passes through the second connection close to the end angle of the second connected ball (17)
Ball (17) is hinged with the first composition panel (1), and the 4th composition panel (4) passes through second close to the end angle of the second connected ball (17)
Connected ball (17) is hinged with the first composition panel (1);
One end of third connecting rod (14) is hinged with the first composition panel (1), the other end and third of third connecting rod (14)
The outer wall of connected ball (18) is slidably matched, and the second composition panel (2) is connected close to the end angle of third connected ball (18) by third
Ball (18) is hinged with the first composition panel (1), and the 6th composition panel (6) passes through third close to the end angle of third connected ball (18)
Connected ball (18) is hinged with the first composition panel (1);
One end of 4th connecting rod (15) is hinged with the first composition panel (1), the other end and the 4th of the 4th connecting rod (15)
The outer wall of connected ball (19) is slidably matched, and the 4th composition panel (4) passes through the 4th connection close to the end angle of the 4th connected ball (19)
Ball (19) is hinged with the first composition panel (1), and the 6th composition panel (6) passes through the 4th close to the end angle of the 4th connected ball (19)
Connected ball (19) is hinged with the first composition panel (1).
5. the study mold of pros' body side surface displaypattern according to claim 4, it is characterised in that:Second composition panel
(2) close to the first connected ball (16) end angle be provided with matched 5th connecting rod (21) of the first connected ball (16), the 5th
Composition panel (5) is provided with and matched 6th connecting rod of the first connected ball (16) close to the end angle of the first connected ball (16)
(22), it is machined on the outer wall of the first connected ball (16) and head rod (12), the 5th connecting rod (21) and the 6th connecting rod
(22) matched chute system, chute system include the first pit (20-1), second dimple (20-2), N annular groove
(20-3) and 2N transition pit (20-4) is machined with the first pit (20-1) on the outer wall of first connected ball (16) respectively
With second dimple (20-2), the first pit (20-1) and second dimple (20-2) are in the same diameter line of the first connected ball (16)
On, 2N transition pit (20-4) is distributed between the first pit (20-1) and second dimple (20-2), every annular groove
(20-3) is connected with the first pit (20-1) and second dimple (20-2) respectively, and every annular groove (20-3) is correspondingly arranged on
Two transition pits (20-4), two corresponding transition pits (20-4) of every annular groove (20-3) are connected.
6. the study mold of pros' body side surface displaypattern according to claim 5, it is characterised in that:Head rod
(12), the 5th connecting rod (21) is identical with the structure of the 6th connecting rod (22), head rod (12) the first connected ball of direction
(16) one end, the 5th connecting rod (21) connect towards one end of the first connected ball (16) and the 6th connecting rod (22) towards first
The receive one end of (16) matches to be formed and the first pit (20-1) or second dimple (20-2) matched connector.
7. 90 ° of rotation process methods that the study mold of pros' body side surface displaypattern according to claim 6 is realized,
It is characterized in that:This method includes:
By first composition panel (1), second composition panel (2), third composition panel (3), the 4th composition panel (4), the 5th group
At panel (5) and the 6th composition panel (6), expansion forms displaypattern in same plane successively;
Selected first composition panel (1), the second composition panel (2), third composition panel (3), the 4th composition panel (4), the 5th
One, two, three or four forms panel rotational structure as a whole in composition panel (5) and the 6th composition panel (6), remains
Remaining composition panel is as fixed structure;
Judge to whether there is 90 ° of angles between unitary rotation structure and fixed structure;
When between unitary rotation structure and fixed structure there are when 90 ° of angles, when unitary rotation structure is rotated, unitary rotation knot
One connection edge of structure and fixed structure separates, after being rotated by 90 °, another connection side of unitary rotation structure and fixed structure
Edge is fitted and connected, that is, forms a kind of square body side surface displaypattern.
8. 90 ° of rotation process methods according to claim 7, it is characterised in that:When unitary rotation structure is the first composition
When panel (1), when judging to be formed with 90 ° of angles between the left side of the first composition panel (1) and other composition panels, first group
Rotation direction at panel (1) is to rotate counterclockwise, and rotational angle is 90 °;Judge the first composition panel (1) right side and its
He forms when being formed with 90 ° of angles between panel, and the rotation direction of the first composition panel (1) is to rotate clockwise, rotational angle
It is 90 °.
9. 90 ° of rotation process methods according to claim 7 or 8, it is characterised in that:When unitary rotation structure includes two
When forming panel, it is disposed adjacent between two composition panels;When unitary rotation structure includes three composition panels, three compositions
Arranged adjacent is arranged successively between panel;When unitary rotation structure include four composition panel when, four composition panels between according to
Secondary arranged adjacent setting.
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CN87210030U (en) * | 1987-07-16 | 1988-03-02 | 斯家伟 | Stereome chess or teaching set |
CN2218089Y (en) * | 1995-01-24 | 1996-01-24 | 郑刚 | Eye protector |
CN1294560A (en) * | 1998-02-25 | 2001-05-09 | 路易斯·布尔戈斯·阿古多 | Versatile container frame with mechanical lid and fixed base for various packaging |
CN202838748U (en) * | 2012-10-17 | 2013-03-27 | 王雪梅 | Solid geometry demonstration teaching aid |
CN205334824U (en) * | 2015-12-16 | 2016-06-22 | 泰山职业技术学院 | Cube expansion teaching aid |
CN206039991U (en) * | 2016-05-03 | 2017-03-22 | 毕蓓 | Solid geometry teaching aid |
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2018
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Publication number | Priority date | Publication date | Assignee | Title |
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CN87210030U (en) * | 1987-07-16 | 1988-03-02 | 斯家伟 | Stereome chess or teaching set |
CN2218089Y (en) * | 1995-01-24 | 1996-01-24 | 郑刚 | Eye protector |
CN1294560A (en) * | 1998-02-25 | 2001-05-09 | 路易斯·布尔戈斯·阿古多 | Versatile container frame with mechanical lid and fixed base for various packaging |
CN202838748U (en) * | 2012-10-17 | 2013-03-27 | 王雪梅 | Solid geometry demonstration teaching aid |
CN205334824U (en) * | 2015-12-16 | 2016-06-22 | 泰山职业技术学院 | Cube expansion teaching aid |
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