MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

18.7 TETRAHEDRON
C = 4 ; V = 4 ; A = 6

Pyramidal TETRAHEDRON

Fig. 1 is the same obtained in Point 18.2.1.1. As a special triangular pyramid, we omit

now its folding diagram.

It is up to the folder to decide the folding mode (valley or mountain) to reach the final

target.

Bi-truncated prism TETRAHEDRON

It is configurated by the union of two equal truncated prisms like those of Point 18.4:

They are positioned crosswise, with the square faces in coincidence (Fig. 3).

Wound up TETRAEDRON

It is similar to the latter that starts with a paper strip containing

just only four equilateral triangles; this, on the contrary, is based in a

triangulated paper strip with many more equilateral triangles.

Fig. 2 shows that strip having 14 triangles to guarantee an effec-

tive final interlock by pocketing the winding end; 8 triangles in the strip

also allow the closing of the tetrahedron, although more precariously.

2

It is evident that the result is a tetrahedron because the slope β = 54,735613 (Points

18.3, 18.4) of one of the truncated prism faces is the same as its opposite side ́s which in turn

is the slope of the side of one tetrahedron (Point 18.2.1.1). In addition we should recall that the

greater side of the truncated prism is double of its bases ́ side: consequently, when completed

the assembly, two sides of the truncated prism base add up to one side of the tetrahedron.

Ex-triangle TETRAHEDRON

Start with an equilateral triangle of center O (Fig. 4) and fold it as shown. The three

OAB type triangles will become the lateral faces, and the three overlapped ABC type will form

the base. To fix the assembly interlock the two last folded triangles by means of the cut lines.

4

C

A B

O

✁ ✁