CN103921478A - 60-degree regular triangular pyramid inserted connection ball - Google Patents
60-degree regular triangular pyramid inserted connection ball Download PDFInfo
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- CN103921478A CN103921478A CN201410164051.8A CN201410164051A CN103921478A CN 103921478 A CN103921478 A CN 103921478A CN 201410164051 A CN201410164051 A CN 201410164051A CN 103921478 A CN103921478 A CN 103921478A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B31—MAKING ARTICLES OF PAPER, CARDBOARD OR MATERIAL WORKED IN A MANNER ANALOGOUS TO PAPER; WORKING PAPER, CARDBOARD OR MATERIAL WORKED IN A MANNER ANALOGOUS TO PAPER
- B31D—MAKING ARTICLES OF PAPER, CARDBOARD OR MATERIAL WORKED IN A MANNER ANALOGOUS TO PAPER, NOT PROVIDED FOR IN SUBCLASSES B31B OR B31C
- B31D5/00—Multiple-step processes for making three-dimensional articles ; Making three-dimensional articles
- B31D5/0086—Making hollow objects
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Abstract
A 60-degree regular triangular pyramid inserted connection ball relates to a three-dimensional shape manufacturing method. The 60-degree regular triangular pyramid inserted connection ball is composed of a first component, a second component, ..., a thirtieth component which are all the same and in inserted connection. A piece of rectangular paper with the ratio between the length and the width as 1.7321:1 is taken to be folded into a parallelogram shape with an interlayer opening and then folded into one component. An inserting triangle part of the first component is inserted into the interlayer opening of an inserted triangle part of the second component, and the inserting triangle part and the inserted triangle part completely coincide with each other to form an equilateral triangle shape. In the same way, the second component is inserted into the third component, the third component is inserted into the first component, and finally a regular triangular pyramid can be finished. In the same way, five regular triangular pyramids can form a pentagon group, and each regular triangular pyramid is one part of three pentagon groups. In the same way, a regular sphere including 20 regular triangular pyramids can be formed, namely the 60-degree regular triangular pyramid inserted connection ball. The 60-degree regular triangular pyramid inserted connection ball is novel and ingenious in idea, simple in component folding, regular and solid in combination and attractive and elegant in appearance.
Description
Technical field
The present invention relates to a kind of preparation method of solid figure, especially a kind of preparation method of the spheroid of pegging graft.
Background technology
At present, the preparation method of the known 60 degree positive triangular pyramid grafting in angle balls, many more complicated, manufacture difficulty is large, and the folding link of parts making is many, causes moulding well-pressed not.
Summary of the invention
In order to overcome the preparation method of the existing 60 degree positive triangular pyramid grafting in angle balls, many more complicated, manufacture difficulty is large, and the folding link of parts making is many, causes the well-pressed not deficiency of moulding, the invention provides a kind of preparation method of the 60 degree positive triangular pyramid grafting in angle balls.
The technical solution adopted for the present invention to solve the technical problems is: the 60 degree positive triangular pyramid grafting in angle balls, by parts 1, parts 2 ... totally 30 same parts grafting of parts 30 combine;
Get the vertical wide rectangular paper of growing crosswise, its Aspect Ratio is 1.7321:1, is also 1:0.5773; Do the diagonal index line of rectangular paper right low left high; Do the vertical line index line vertical with diagonal index line at the mid point of diagonal index line, intersect at upper trimming intersection point with trimming in rectangular paper, intersect at lower trimming intersection point with lower trimming; Above trimming, upper trimming intersection point is boundary, and left section is left section of upper trimming, and right section is right section of upper trimming; Following trimming, lower trimming intersection point is boundary, and left section is left section of lower trimming, and right section is right section of lower trimming; The angular bisector that does left section of trimming and vertical line index line angle, i.e. the positive broken line of left comer bisector, intersects at left trimming intersection point with the left trimming of rectangular paper; The angular bisector that does right section of lower trimming and vertical line index line angle, i.e. the positive broken line of right corner bisector, intersects at right trimming intersection point with the right trimming of rectangular paper; Yi Zuo trimming, left trimming intersection point is boundary, and epimere is left trimming epimere, and hypomere is left trimming hypomere; Yi You trimming, right trimming intersection point is boundary, and epimere is right trimming epimere, and hypomere is right trimming hypomere; Between left trimming intersection point and lower trimming intersection point, do line, i.e. the positive broken line of left line; Between right trimming intersection point and upper trimming intersection point, do line, i.e. the positive broken line of right line;
According to the positive broken line of left line and the positive broken line of right line, the lower left corner and the upper right corner are folded and are affixed to the middle part of rectangular paper, left trimming hypomere overlaps with the positive broken line of left comer bisector, and right trimming epimere overlaps with the positive broken line of right corner bisector; The positive broken line of left line is changed to left line sideline, and the positive broken line of right line is changed to right line sideline;
According to the positive broken line of left comer bisector and the positive broken line of right corner bisector, the upper left corner of rectangular paper and the lower right corner are folded and are affixed to the middle part of rectangular paper, left section of upper trimming, right section of lower trimming and vertical line index line overlap as coincidence vertical line index line, and form interlayer opening; Left trimming epimere overlaps with left line sideline, and right trimming epimere overlaps with right line sideline; Rectangular paper is deformed into flat shape quadrangle, and the positive broken line of left comer bisector is its left long limit, and the positive broken line of right corner bisector is its right long limit, and coincidence vertical line index line is the tetragonal obtuse angle of flat shape diagonal; Do perpendicular to the positive broken line of the cornerwise vertical line in obtuse angle at obtuse angle diagonal mid point, intersect at left long limit intersection point with left long limit, intersect at right long limit intersection point with right long limit; Between the intersection point of the Yu Youchang limit, summit, upper obtuse angle of parallelogram, do line, i.e. right line fold line is done line, i.e. left line fold line between the intersection point of Yu Zuochang limit, summit, lower obtuse angle; Flat shape quadrangle is divided into four congruent equilateral triangles by left line fold line, right line fold line and the positive broken line of vertical line; The triangle of flat shape quadrangle acute angle portion is for inserting triangle, and two triangles that have interlayer opening at middle part are for being inserted into triangle;
Folding according to left line fold line, right line fold line and the positive broken line of vertical line, parts;
Insert triangle by one of parts 1, of insertion parts 2 is inserted into the interlayer opening of triangle, and inserting trigonometric sum, to be inserted into that triangle overlaps be completely an equilateral triangle, completed once and pegged graft;
Peg graft in this way, the interlayer opening that is inserted into of the connected insertion triangle insertion parts 3 of triangle and is inserted into triangle of parts 2, parts 3 be inserted into the connected insertion triangle insertion parts 1 of triangle insert triangle be connected the interlayer opening that is inserted into triangle, complete the grafting of a positive triangular pyramid;
The not grafting part of having pegged graft into one of them parts of positive triangular pyramid continues to peg graft with parts 4, parts 5, second the positive triangular pyramid of pegging graft out; Peg graft in this way, peg graft out the 3rd, the 4th ... positive triangular pyramid; Five positive triangular pyramids are one group of i.e. five jiaos of group, and each positive triangular pyramid is in three five jiaos of groups; Peg graft in this way, peg graft into the sphere body of 20 positive triangular pyramids, be i.e. the 60 degree positive triangular pyramid grafting in angle balls.
The invention has the beneficial effects as follows, novel ingenious, parts are folding simple, and rule of combination is solid, handsome in appearance well-pressed.
Brief description of the drawings
Below in conjunction with drawings and Examples, the present invention is further described.
Fig. 1 is the rectangular paper plane that is decorated with fold line;
Fig. 2 is the plane after the lower left corner, the upper right corner fold;
Fig. 3 is flat shape quadrangular plan figure;
Fig. 4 is parts stereograms;
Fig. 5 is two parts grafting schematic diagrames;
Fig. 6 is a positive triangular pyramid stereogram;
Fig. 7 is the 60 positive triangular pyramid grafting in degree angle ball stereograms.
Detailed description of the invention
The 60 degree positive triangular pyramid grafting in angle balls, by parts 1, parts 2 ... totally 30 same parts grafting of parts 30 combine; Adopt the positive broken line that dots positive doubling, solid line adds the fold line that circle represents reverse side doubling; The solid line expression index line of adding some points; Arrow line represents to insert line, and the dotted portion of arrow line represents insertion portion, and the solid line part of arrow line represents not insertion portion;
Get the vertical wide rectangular paper of growing crosswise, its Aspect Ratio is 1.7321:1, is also 1:0.5773; Do the diagonal index line of rectangular paper right low left high; Do the vertical line index line vertical with diagonal index line at the mid point of diagonal index line, intersect at upper trimming intersection point with trimming in rectangular paper, intersect at lower trimming intersection point with lower trimming; Above trimming, upper trimming intersection point is boundary, and left section is left section of upper trimming, and right section is right section of upper trimming; Following trimming, lower trimming intersection point is boundary, and left section is left section of lower trimming, and right section is right section of lower trimming; The angular bisector that does left section of trimming and vertical line index line angle, i.e. the positive broken line of left comer bisector, intersects at left trimming intersection point with the left trimming of rectangular paper; The angular bisector that does right section of lower trimming and vertical line index line angle, i.e. the positive broken line of right corner bisector, intersects at right trimming intersection point with the right trimming of rectangular paper; Yi Zuo trimming, left trimming intersection point is boundary, and epimere is left trimming epimere, and hypomere is left trimming hypomere; Yi You trimming, right trimming intersection point is boundary, and epimere is right trimming epimere, and hypomere is right trimming hypomere; Between left trimming intersection point and lower trimming intersection point, do line, i.e. the positive broken line of left line; Do line, i.e. the positive broken line of right line right trimming intersection point and asking of upper trimming intersection point; As Fig. 1;
According to the positive broken line of left line and the positive broken line of right line, the lower left corner and the upper right corner are folded and are affixed to the middle part of rectangular paper, left trimming hypomere overlaps with the positive broken line of left comer bisector, and right trimming epimere overlaps with the positive broken line of right corner bisector; The positive broken line of left line is changed to left line sideline, and the positive broken line of right line is changed to right line sideline; As Fig. 2;
According to the positive broken line of left comer bisector and the positive broken line of right corner bisector, the upper left corner of rectangular paper and the lower right corner are folded and are affixed to the middle part of rectangular paper, left section of upper trimming, right section of lower trimming and vertical line index line overlap as coincidence vertical line index line, and form interlayer opening; Left trimming epimere overlaps with left line sideline, and right trimming epimere overlaps with right line sideline; Rectangular paper is deformed into flat shape quadrangle, and the positive broken line of left comer bisector is its left long limit, and the positive broken line of right corner bisector is its right long limit, and coincidence vertical line index line is the tetragonal obtuse angle of flat shape diagonal; Do perpendicular to the positive broken line of the cornerwise vertical line in obtuse angle at obtuse angle diagonal mid point, intersect at left long limit intersection point with left long limit, intersect at right long limit intersection point with right long limit; Between the intersection point of the Yu Youchang limit, summit, upper obtuse angle of parallelogram, do line, i.e. right line fold line is done line, i.e. left line fold line between the intersection point of Yu Zuochang limit, summit, lower obtuse angle; Flat shape quadrangle is divided into four congruent equilateral triangles by left line fold line, right line fold line and the positive broken line of vertical line; The triangle of flat shape quadrangle acute angle portion is for inserting triangle, and two triangles that have interlayer opening at middle part are for being inserted into triangle; As Fig. 3;
Folding according to left line fold line, right line fold line and the positive broken line of vertical line, parts; As Fig. 4;
Insert triangle by one of parts 1, of insertion parts 2 is inserted into the interlayer opening of triangle, and inserting trigonometric sum, to be inserted into that triangle overlaps be completely an equilateral triangle, completed once and pegged graft; As Fig. 5;
Peg graft in this way, the interlayer opening that is inserted into of the connected insertion triangle insertion parts 3 of triangle and is inserted into triangle of parts 2, parts 3 be inserted into the connected insertion triangle insertion parts 1 of triangle insert triangle be connected the interlayer opening that is inserted into triangle, complete the grafting of a positive triangular pyramid; As Fig. 6;
The not grafting part of having pegged graft into one of them parts of positive triangular pyramid continues to peg graft with parts 4, parts 5, second the positive triangular pyramid of pegging graft out; Peg graft in this way, peg graft out the 3rd, the 4th ... positive triangular pyramid; Five positive triangular pyramids are one group of i.e. five jiaos of group, and each positive triangular pyramid is in three five jiaos of groups; Peg graft in this way, peg graft into the sphere body of 20 positive triangular pyramids, be i.e. the 60 degree positive triangular pyramid grafting in angle balls; As Fig. 7.
Claims (1)
1. the 60 degree positive triangular pyramid grafting in angle balls, is characterized in that: the 60 degree positive triangular pyramid grafting in angle balls, by parts 1, parts 2 ... totally 30 same parts grafting of parts 30 combine;
Get the vertical wide rectangular paper of growing crosswise, its Aspect Ratio is 1.7321:1, is also 1:0.5773; Do the diagonal index line of rectangular paper right low left high; Do the vertical line index line vertical with diagonal index line at the mid point of diagonal index line, intersect at upper trimming intersection point with trimming in rectangular paper, intersect at lower trimming intersection point with lower trimming; Above trimming, upper trimming intersection point is boundary, and left section is left section of upper trimming, and right section is right section of upper trimming; Following trimming, lower trimming intersection point is boundary, and left section is left section of lower trimming, and right section is right section of lower trimming; The angular bisector that does left section of trimming and vertical line index line angle, i.e. the positive broken line of left comer bisector, intersects at left trimming intersection point with the left trimming of rectangular paper; The angular bisector that does right section of lower trimming and vertical line index line angle, i.e. the positive broken line of right corner bisector, intersects at right trimming intersection point with the right trimming of rectangular paper; Yi Zuo trimming, left trimming intersection point is boundary, and epimere is left trimming epimere, and hypomere is left trimming hypomere; Yi You trimming, right trimming intersection point is boundary, and epimere is right trimming epimere, and hypomere is right trimming hypomere; Between left trimming intersection point and lower trimming intersection point, do line, i.e. the positive broken line of left line; Between right trimming intersection point and upper trimming intersection point, do line, i.e. the positive broken line of right line;
According to the positive broken line of left line and the positive broken line of right line, the lower left corner and the upper right corner are folded and are affixed to the middle part of rectangular paper, left trimming hypomere overlaps with the positive broken line of left comer bisector, and right trimming epimere overlaps with the positive broken line of right corner bisector; The positive broken line of left line is changed to left line sideline, and the positive broken line of right line is changed to right line sideline;
According to the positive broken line of left comer bisector and the positive broken line of right corner bisector, the upper left corner of rectangular paper and the lower right corner are folded and are affixed to the middle part of rectangular paper, left section of upper trimming, right section of lower trimming and vertical line index line overlap as coincidence vertical line index line, and form interlayer opening; Left trimming epimere overlaps with left line sideline, and right trimming epimere overlaps with right line sideline; Rectangular paper is deformed into flat shape quadrangle, and the positive broken line of left comer bisector is its left long limit, and the positive broken line of right corner bisector is its right long limit, and coincidence vertical line index line is the tetragonal obtuse angle of flat shape diagonal; Do perpendicular to the positive broken line of the cornerwise vertical line in obtuse angle at obtuse angle diagonal mid point, intersect at left long limit intersection point with left long limit, intersect at right long limit intersection point with right long limit; Between the intersection point of the Yu Youchang limit, summit, upper obtuse angle of parallelogram, do line, i.e. right line fold line is done line, i.e. left line fold line between the intersection point of Yu Zuochang limit, summit, lower obtuse angle; Flat shape quadrangle is divided into four congruent equilateral triangles by left line fold line, right line fold line and the positive broken line of vertical line; The triangle of flat shape quadrangle acute angle portion is for inserting triangle, and two triangles that have interlayer opening at middle part are for being inserted into triangle;
Folding according to left line fold line, right line fold line and the positive broken line of vertical line, parts;
Insert triangle by one of parts 1, of insertion parts 2 is inserted into the interlayer opening of triangle, and inserting trigonometric sum, to be inserted into that triangle overlaps be completely an equilateral triangle, completed once and pegged graft;
Peg graft in this way, the interlayer opening that is inserted into of the connected insertion triangle insertion parts 3 of triangle and is inserted into triangle of parts 2, parts 3 be inserted into the connected insertion triangle insertion parts 1 of triangle insert triangle be connected the interlayer opening that is inserted into triangle, complete the grafting of a positive triangular pyramid;
The not grafting part of having pegged graft into one of them parts of positive triangular pyramid continues to peg graft with parts 4, parts 5, second the positive triangular pyramid of pegging graft out; Peg graft in this way, peg graft out the 3rd, the 4th ... positive triangular pyramid; Five positive triangular pyramids are one group of i.e. five jiaos of group, and each positive triangular pyramid is in three five jiaos of groups; Peg graft in this way, peg graft into the sphere body of 20 positive triangular pyramids, be i.e. the 60 degree positive triangular pyramid grafting in angle balls.
Priority Applications (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410164051.8A CN103921478B (en) | 2014-04-08 | 2014-04-08 | The 60 degree positive triangular pyramid grafting in angle balls |
| PCT/CN2015/075545 WO2015154632A1 (en) | 2014-04-08 | 2015-03-31 | Sphere of 60-degree regular triangular pyramids connected by insertion |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410164051.8A CN103921478B (en) | 2014-04-08 | 2014-04-08 | The 60 degree positive triangular pyramid grafting in angle balls |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN103921478A true CN103921478A (en) | 2014-07-16 |
| CN103921478B CN103921478B (en) | 2016-05-18 |
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Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201410164051.8A Expired - Fee Related CN103921478B (en) | 2014-04-08 | 2014-04-08 | The 60 degree positive triangular pyramid grafting in angle balls |
Country Status (2)
| Country | Link |
|---|---|
| CN (1) | CN103921478B (en) |
| WO (1) | WO2015154632A1 (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104626656A (en) * | 2015-01-27 | 2015-05-20 | 李平 | Square frame |
| WO2015154632A1 (en) * | 2014-04-08 | 2015-10-15 | 罗明镜 | Sphere of 60-degree regular triangular pyramids connected by insertion |
| CN107531355A (en) * | 2015-03-17 | 2018-01-02 | 耐克创新有限合伙公司 | Demonstration package |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2011097155A1 (en) * | 2010-02-03 | 2011-08-11 | Benjamin John Coleman | A folding pattern |
| CN103465518A (en) * | 2013-09-07 | 2013-12-25 | 李平 | Manufacturing method for three-component regular-triangular platy body |
| CN103481547A (en) * | 2013-09-14 | 2014-01-01 | 李平 | Production method of three-assembly equilateral triangle paper sheet body |
| CN103522599A (en) * | 2013-10-19 | 2014-01-22 | 李平 | Method of folding 45-degree acutely angled diamond insert |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE3618092A1 (en) * | 1985-06-03 | 1986-12-04 | Europäische-Festländische Brüder-Unität Körperschaft des öffentlichen Rechts, 7325 Bad Boll | Folding star |
| CN103921478B (en) * | 2014-04-08 | 2016-05-18 | 范鲁杰 | The 60 degree positive triangular pyramid grafting in angle balls |
-
2014
- 2014-04-08 CN CN201410164051.8A patent/CN103921478B/en not_active Expired - Fee Related
-
2015
- 2015-03-31 WO PCT/CN2015/075545 patent/WO2015154632A1/en active Application Filing
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2011097155A1 (en) * | 2010-02-03 | 2011-08-11 | Benjamin John Coleman | A folding pattern |
| CN103465518A (en) * | 2013-09-07 | 2013-12-25 | 李平 | Manufacturing method for three-component regular-triangular platy body |
| CN103481547A (en) * | 2013-09-14 | 2014-01-01 | 李平 | Production method of three-assembly equilateral triangle paper sheet body |
| CN103522599A (en) * | 2013-10-19 | 2014-01-22 | 李平 | Method of folding 45-degree acutely angled diamond insert |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2015154632A1 (en) * | 2014-04-08 | 2015-10-15 | 罗明镜 | Sphere of 60-degree regular triangular pyramids connected by insertion |
| CN104626656A (en) * | 2015-01-27 | 2015-05-20 | 李平 | Square frame |
| CN107531355A (en) * | 2015-03-17 | 2018-01-02 | 耐克创新有限合伙公司 | Demonstration package |
Also Published As
| Publication number | Publication date |
|---|---|
| WO2015154632A1 (en) | 2015-10-15 |
| CN103921478B (en) | 2016-05-18 |
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Inventor after: Fan Lujie Inventor before: Li Bopan |
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Effective date of registration: 20160419 Address after: College of science and technology Weifang 166 No. 262700 Shandong Shouguang City of Weifang province Xueyuan Road Applicant after: Fan Lujie Address before: 570105 Binhai Road, Longhua District, Hainan, China, No. 61, No. Applicant before: Li Bopan |
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