CN103921478B - The 60 degree positive triangular pyramid grafting in angle balls - Google Patents
The 60 degree positive triangular pyramid grafting in angle balls Download PDFInfo
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- CN103921478B CN103921478B CN201410164051.8A CN201410164051A CN103921478B CN 103921478 B CN103921478 B CN 103921478B CN 201410164051 A CN201410164051 A CN 201410164051A CN 103921478 B CN103921478 B CN 103921478B
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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 kind of 60 spend the positive triangular pyramid grafting in angle balls, relate to a kind of preparation method of solid figure. 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 rectangular paper of Aspect Ratio 1.7321:1, be folded into the flat shape quadrangle of interlayer opening, and and then be folded into 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; Peg graft in this way, parts 2 insertion parts 3, parts 3 insertion parts 1, complete the grafting of a positive triangular pyramid; Peg graft in this way, 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; Novel ingenious, parts are folding simple, and rule of combination is solid, handsome in appearance well-pressed.
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, parts systemMake folding link many, cause 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, partsMake folding link many, cause the well-pressed not deficiency of moulding, the invention provides a kind of system of the 60 degree positive triangular pyramid grafting in angle ballsMake method.
The technical solution adopted for the present invention to solve the technical problems is: the 60 degree positive triangular pyramid grafting in angle balls, and by parts 1, portionPart 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 rectangular paper right low left highDiagonal index line; Do the vertical line index line vertical with diagonal index line at the mid point of diagonal index line, with rectangleOn paper, trimming intersects at trimming intersection point, intersects at lower trimming intersection point with lower trimming; Above trimming, upper trimming intersection point is boundary, a left sideSection 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, the right sideSection is right section of lower trimming; Do the angular bisector of left section of trimming and vertical line index line angle, i.e. the positive broken line of left comer bisector,Intersect at left trimming intersection point with the left trimming of rectangular paper; Do the angular bisector of right section of lower trimming and vertical line index line angle,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, onSection 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, underSection 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; Hand on right trimmingBetween 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, a left sideTrimming 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 lineBe changed to left line sideline, 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, by the upper left corner of rectangular paper and the lower right corner to rectangular paperMiddle part is folding to be affixed, and left section of upper trimming, right section of lower trimming and vertical line index line overlap as coincidence vertical line index line, and shapeBecome interlayer opening; Left trimming epimere overlaps with left line sideline, and right trimming epimere overlaps with right line sideline; Rectangular paper distortionFor flat shape quadrangle, 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, overlaps verticalLine index line is the tetragonal obtuse angle of flat shape diagonal; Perpendicular to the cornerwise vertical line in obtuse angle just do at obtuse angle diagonal mid pointBroken line, intersects at left long limit intersection point with left long limit, intersects at right long limit intersection point with right long limit; At the upper obtuse angle of parallelogramBetween the intersection point of Yu Youchang limit, summit, do line, i.e. right line fold line is done line between the intersection point of Yu Zuochang limit, summit, lower obtuse angle,It is left line fold line; Flat shape quadrangle is divided into four by left line fold line, right line fold line and the positive broken line of vertical lineThe equilateral triangle of congruence; The triangle of flat shape quadrangle acute angle portion is for inserting triangle, have interlayer opening two of middle partTriangle is 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, inserts trigonometric sum quiltIt is an equilateral triangle that insertion triangle overlaps completely, has completed once and has pegged graft;
Peg graft in this way, the folder that is inserted into of the connected insertion triangle insertion parts 3 of triangle and is inserted into triangle of parts 2Layer opening, parts 3 be inserted into the connected insertion triangle insertion parts 1 of triangle insert triangle be connected be inserted into threeThe interlayer opening at angle, completes 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, pegs graft outSecond positive triangular pyramid; Peg graft in this way, peg graft out the 3rd, the 4th ... positive triangular pyramid; Five positive triangular pyramids are oneGroup i.e. five jiaos of groups, and each positive triangular pyramid is in three five jiaos of groups; Peg graft in this way, peg graft into 20 positive Rhizoma SparganiisThe sphere body of cone, the i.e. 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 sectionPoint;
Get the vertical wide rectangular paper of growing crosswise, its Aspect Ratio is 1.7321:1, is also 1:0.5773; Do rectangular paper right low left highDiagonal index line; Do the vertical line index line vertical with diagonal index line at the mid point of diagonal index line, with rectangleOn paper, trimming intersects at trimming intersection point, intersects at lower trimming intersection point with lower trimming; Above trimming, upper trimming intersection point is boundary, a left sideSection 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, the right sideSection is right section of lower trimming; Do the angular bisector of left section of trimming and vertical line index line angle, i.e. the positive broken line of left comer bisector,Intersect at left trimming intersection point with the left trimming of rectangular paper; Do the angular bisector of right section of lower trimming and vertical line index line angle,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, onSection 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, underSection 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; Hand on right trimmingPoint does line, i.e. the positive broken line of right line with 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, a left sideTrimming 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 lineBe changed to left line sideline, 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, by the upper left corner of rectangular paper and the lower right corner to rectangular paperMiddle part is folding to be affixed, and left section of upper trimming, right section of lower trimming and vertical line index line overlap as coincidence vertical line index line, and shapeBecome interlayer opening; Left trimming epimere overlaps with left line sideline, and right trimming epimere overlaps with right line sideline; Rectangular paper distortionFor flat shape quadrangle, 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, overlaps verticalLine index line is the tetragonal obtuse angle of flat shape diagonal; Perpendicular to the cornerwise vertical line in obtuse angle just do at obtuse angle diagonal mid pointBroken line, intersects at left long limit intersection point with left long limit, intersects at right long limit intersection point with right long limit; At the upper obtuse angle of parallelogramBetween the intersection point of Yu Youchang limit, summit, do line, i.e. right line fold line is done line between the intersection point of Yu Zuochang limit, summit, lower obtuse angle,It is left line fold line; Flat shape quadrangle is divided into four by left line fold line, right line fold line and the positive broken line of vertical lineThe equilateral triangle of congruence; The triangle of flat shape quadrangle acute angle portion is for inserting triangle, have interlayer opening two of middle partTriangle is 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, inserts trigonometric sum quiltIt is an equilateral triangle that insertion triangle overlaps completely, has completed once and has pegged graft; As Fig. 5;
Peg graft in this way, the folder that is inserted into of the connected insertion triangle insertion parts 3 of triangle and is inserted into triangle of parts 2Layer opening, parts 3 be inserted into the connected insertion triangle insertion parts 1 of triangle insert triangle be connected be inserted into threeThe interlayer opening at angle, completes 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, pegs graft outSecond positive triangular pyramid; Peg graft in this way, peg graft out the 3rd, the 4th ... positive triangular pyramid; Five positive triangular pyramids are oneGroup i.e. five jiaos of groups, and each positive triangular pyramid is in three five jiaos of groups; Peg graft in this way, peg graft into 20 positive Rhizoma SparganiisThe sphere body of cone, the i.e. 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, and by parts 1, portionPart 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 rectangular paper right low left highDiagonal index line; Do the vertical line index line vertical with diagonal index line at the mid point of diagonal index line, with rectangleOn paper, trimming intersects at trimming intersection point, intersects at lower trimming intersection point with lower trimming; Above trimming, upper trimming intersection point is boundary, a left sideSection 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, the right sideSection is right section of lower trimming; Do the angular bisector of left section of trimming and vertical line index line angle, i.e. the positive broken line of left comer bisector,Intersect at left trimming intersection point with the left trimming of rectangular paper; Do the angular bisector of right section of lower trimming and vertical line index line angle,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, onSection 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, underSection 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; Hand on right trimmingBetween 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, a left sideTrimming 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 lineBe changed to left line sideline, 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, by the upper left corner of rectangular paper and the lower right corner to rectangular paperMiddle part is folding to be affixed, and left section of upper trimming, right section of lower trimming and vertical line index line overlap as coincidence vertical line index line, and shapeBecome interlayer opening; Left trimming epimere overlaps with left line sideline, and right trimming epimere overlaps with right line sideline; Rectangular paper distortionFor flat shape quadrangle, 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, overlaps verticalLine index line is the tetragonal obtuse angle of flat shape diagonal; Perpendicular to the cornerwise vertical line in obtuse angle just do at obtuse angle diagonal mid pointBroken line, intersects at left long limit intersection point with left long limit, intersects at right long limit intersection point with right long limit; At the upper obtuse angle of parallelogramBetween the intersection point of Yu Youchang limit, summit, do line, i.e. right line fold line is done line between the intersection point of Yu Zuochang limit, summit, lower obtuse angle,It is left line fold line; Flat shape quadrangle is divided into four by left line fold line, right line fold line and the positive broken line of vertical lineThe equilateral triangle of congruence; The triangle of flat shape quadrangle acute angle portion is for inserting triangle, have interlayer opening two of middle partTriangle is 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, inserts trigonometric sum quiltIt is an equilateral triangle that insertion triangle overlaps completely, has completed once and has pegged graft;
Peg graft in this way, the folder that is inserted into of the connected insertion triangle insertion parts 3 of triangle and is inserted into triangle of parts 2Layer opening, parts 3 be inserted into the connected insertion triangle insertion parts 1 of triangle insert triangle be connected be inserted into threeThe interlayer opening at angle, completes 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, pegs graft outSecond positive triangular pyramid; Peg graft in this way, peg graft out the 3rd, the 4th ... positive triangular pyramid; Five positive triangular pyramids are oneGroup i.e. five jiaos of groups, and each positive triangular pyramid is in three five jiaos of groups; Peg graft in this way, peg graft into 20 positive Rhizoma SparganiisThe sphere body of cone, the i.e. 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 CN103921478A (en) | 2014-07-16 |
| CN103921478B true CN103921478B (en) | 2016-05-18 |
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| 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) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103921478B (en) * | 2014-04-08 | 2016-05-18 | 范鲁杰 | The 60 degree positive triangular pyramid grafting in angle balls |
| CN104626656A (en) * | 2015-01-27 | 2015-05-20 | 李平 | Square frame |
| US9643747B2 (en) * | 2015-03-17 | 2017-05-09 | Nike, Inc. | Display packaging |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 (3)
| 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 |
| US8545286B2 (en) * | 2010-02-03 | 2013-10-01 | Benjamin John Coleman | Folding pattern |
| 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
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2015
- 2015-03-31 WO PCT/CN2015/075545 patent/WO2015154632A1/en active Application Filing
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
Also Published As
| Publication number | Publication date |
|---|---|
| WO2015154632A1 (en) | 2015-10-15 |
| CN103921478A (en) | 2014-07-16 |
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| C41 | Transfer of patent application or patent right or utility model | ||
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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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