CN103847137A - Method for preparing regular tetrahedron - Google Patents

Abstract

The invention discloses a method for preparing a regular tetrahedron, and relates to a method for preparing a paper vessel. The regular tetrahedron is formed by splicing four same components, wherein each component is formed by combining a part A and a part B, and a congruent triangle is formed by overlapping and folding the part A and the part B; and then a cube, which are 60 degrees in three planes and takes a central point as a peak, is formed by folding the congruent triangle, and three small triangles A are formed in a folding way, so as to form a folded insertion angle with two planes at the angle of 30 degrees, and forming a component folded and inserted into the opening of an interlayer through common edges A; the folded insertion angle of one component is inserted into the opening of the interlayer of the other component, so that the inserted connection that one folding insertion angle of one component and the fold of the other component are inserted into the opening of the interlayer can be finished, and the two components can be connected with each other in an inserting way; and four components are connected with each other in pairs in an inserting way, so as to form the regular tetrahedron. The method is strange and exquisite in concept and simple to design; furthermore, the components are standardly prepared, and the inserted connection of the components is regular and orderly; and the spliced regular tetrahedron is firm and is unlikely to deform.

Description

A kind of preparation method of positive tetrahedron

Technical field

The present invention relates to a kind of preparation method of solid, especially a kind of tetrahedral preparation method.

Background technology

At present, the preparation method of known positive tetrahedron, what have is accurate not, and what have is solid not, and what have is too complicated, and manufacture difficulty is larger.

Summary of the invention

In order to overcome the preparation method of existing positive tetrahedron, what have is accurate not, and what have is solid not, and what have is too complicated, and the deficiency that manufacture difficulty is larger the invention provides a kind of preparation method of positive tetrahedron.

The technical solution adopted for the present invention to solve the technical problems is: positive tetrahedron is pegged graft and formed by four same components; Each assembly is formed by A part B component combination; Getting equilateral triangle, under an angle, is A parts;

Getting and the equilateral triangle of A parts congruence, on an angle, is B parts;

B parts are placed on A parts, and lap forms regular hexagon, and positive hexagon is six little equilateral triangles of congruence outside opening, i.e. three little triangles of B of three of A parts little triangles of A and B parts; The common limit of the little triangle of A and regular hexagon is the common limit of A, and the common limit of the little triangle of B and regular hexagon is the common limit of B; On the common limit of B, do the little triangle fold line of B;

According to the little triangle fold line of B, little B triangle collapse is affixed, with the congruent triangles of A parts congruence; Vertical line fold line is done to opposite side in summit by the angle of congruent triangles, intersects at opposite side mid point with opposite side, intersects at A intersection point with the common limit of A, and three vertical line fold lines intersect at congruent triangles center, i.e. central point; On vertical line fold line, the summit at congruent triangles angle is to being vertical line fold line between central point, and central point is between opposite side mid point being the positive broken line of vertical line; Take central point as basic point, vertical line fold line is pointer, does angular bisector fold line by vertical line fold line and the angle that the counterclockwise nearest positive broken line of vertical line forms, crossing with an end points on the common limit of A;

Fold and be affixed according to vertical line fold line, the positive broken line of vertical line, angular bisector fold line, three planes take central point as summit be the cube at 60 degree angles, three little triangles of A form rugosity, after folding, two planes of formation are the folding insertion angle at 30 degree angles, and the common limit of A forms the folding interlayer opening that is inserted into; An assembly completes;

The folding of another assembly inserted in the folding insertion angle of an assembly and be inserted in interlayer opening, completed a folding folding grafting that is inserted into interlayer opening of inserting angle and another assembly of an assembly; Four assemblies are pegged graft between two mutually, form the preliminary shape of positive tetrahedron;

Four assemblies are pegged graft between two mutually, the docking until the interlayer opening of two assemblies that plug coincides, positive tetrahedron.

The invention has the beneficial effects as follows, conceive new and ingenious, simplicity of design; Establishment of component standard, the grafting rule of assembly is orderly; The positive tetrahedron that grafting forms is solid and not yielding.

Accompanying drawing explanation

Below in conjunction with drawings and Examples, the present invention is further described.

Fig. 1 is A parts planes;

Fig. 2 is B parts planes;

Fig. 3 is placed in B parts on A parts, and lap forms orthohexagonal plane;

Fig. 4 is congruent triangles plane;

Fig. 5 is assembly stereogram;

Fig. 6 is four modular connector schematic diagrames;

Fig. 7 is positive tetrahedron stereogram;

The specific embodiment

Positive tetrahedron is pegged graft and is formed by four same components; Each assembly is formed by A part B component combination; Adopt the positive broken line that dots positive doubling, solid line adds the fold line that circle represents reverse side doubling;

Getting equilateral triangle, under an angle, is A parts; As Fig. 1;

Getting and the equilateral triangle of A parts congruence, on an angle, is B parts; As Fig. 2;

B parts are placed on A parts, and lap forms regular hexagon, and positive hexagon is six little equilateral triangles of congruence outside opening, i.e. three little triangles of B of three of A parts little triangles of A and B parts; The common limit of the little triangle of A and regular hexagon is the common limit of A, and the common limit of the little triangle of B and regular hexagon is the common limit of B; On the common limit of B, do the little triangle fold line of B; As Fig. 3;

According to the little triangle fold line of B, little B triangle collapse is affixed, with the congruent triangles of A parts congruence; Vertical line fold line is done to opposite side in summit by the angle of congruent triangles, intersects at opposite side mid point with opposite side, intersects at A intersection point with the common limit of A, and three vertical line fold lines intersect at congruent triangles center, i.e. central point; On vertical line fold line, the summit at congruent triangles angle is to being vertical line fold line between central point, and central point is between opposite side mid point being the positive broken line of vertical line; Take central point as basic point, vertical line fold line is pointer, does angular bisector fold line by vertical line fold line and the angle that the counterclockwise nearest positive broken line of vertical line forms, crossing with an end points on the common limit of A; As Fig. 4;

Fold and be affixed according to vertical line fold line, the positive broken line of vertical line, angular bisector fold line, three planes take central point as summit be the cube at 60 degree angles, three little triangles of A form rugosity, after folding, two planes of formation are the folding insertion angle at 30 degree angles, and the common limit of A forms the folding interlayer opening that is inserted into; An assembly completes; As Fig. 5;

The folding of another assembly inserted in the folding insertion angle of an assembly and be inserted in interlayer opening, completed a folding folding grafting that is inserted into interlayer opening of inserting angle and another assembly of an assembly, two assemblies can be pegged graft each other; Four assemblies are pegged graft between two mutually, form the preliminary shape of positive tetrahedron; As Fig. 6;

Four assemblies are pegged graft between two mutually, the docking until the interlayer opening of two assemblies that plug coincides, positive tetrahedron; As Fig. 7.

Claims (1)

1. a preparation method for positive tetrahedron, is characterized in that: positive tetrahedron is pegged graft and formed by four same components; Each assembly is formed by A part B component combination; Getting equilateral triangle, under an angle, is A parts;

Getting and the equilateral triangle of A parts congruence, on an angle, is B parts;

B parts are placed on A parts, and lap forms regular hexagon, and positive hexagon is six little equilateral triangles of congruence outside opening, i.e. three little triangles of B of three of A parts little triangles of A and B parts; The common limit of the little triangle of A and regular hexagon is the common limit of A, and the common limit of the little triangle of B and regular hexagon is the common limit of B; On the common limit of B, do the little triangle fold line of B;

According to the little triangle fold line of B, little B triangle collapse is affixed, with the congruent triangles of A parts congruence; Vertical line fold line is done to opposite side in summit by the angle of congruent triangles, intersects at opposite side mid point with opposite side, intersects at A intersection point with the common limit of A, and three vertical line fold lines intersect at congruent triangles center, i.e. central point; On vertical line fold line, the summit at congruent triangles angle is to being vertical line fold line between central point, and central point is between opposite side mid point being the positive broken line of vertical line; Take central point as basic point, vertical line fold line is pointer, does angular bisector fold line by vertical line fold line and the angle that the counterclockwise nearest positive broken line of vertical line forms, crossing with an end points on the common limit of A;

Fold and be affixed according to vertical line fold line, the positive broken line of vertical line, angular bisector fold line, three planes take central point as summit be the cube at 60 degree angles, three little triangles of A form rugosity, after folding, two planes of formation are the folding insertion angle at 30 degree angles, and the common limit of A forms the folding interlayer opening that is inserted into; An assembly completes;

The folding of another assembly inserted in the folding insertion angle of an assembly and be inserted in interlayer opening, completed a folding folding grafting that is inserted into interlayer opening of inserting angle and another assembly of an assembly; Four assemblies are pegged graft between two mutually, form the preliminary shape of positive tetrahedron;

Four assemblies are pegged graft between two mutually, the docking until the interlayer opening of two assemblies that plug coincides, positive tetrahedron.

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