MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

18.9 OCTAHEDRON
C = 8 ; V = 6 ; A = 12
18.9.1 Bipyramidal OCTAEDRON

18.9.2 Wound up OCTAHEDRON

Start with a triangulated paper strip of 26 equilateral triangles (most likely we shall have

to join several individual strips). Every crease has to be docile to mountain as well as to va-

18.9.3 Ex-tetrahedron OCTAHEDRON

2

3

3

= ×

l

a ; 0 , 8164965

36

3

4

3

H=l − =l

According to (Fig. 1) it is made out

of two opposed equal quadrangular pyra-

mids (see Point 18.2.2.2).

lley fold indistinctly. Start from one end of the

strip to get an octahedron like that shown in Fig.

1 which lacks two opposite faces. Continue

winding the strip over the octahedron till the

moment the last triangle can be pocked into the

corresponding slot. Less than 26 triangles may

lead to a precarious structure; with more than 26

we face a problematic construction because of

paper accumulation.

Fig.1shows an octahedron built from a tetrahe-

dron whose 4 vertices have been flattened out by pleat

folding. Fig. 3 is the tetrahedron folding diagram in-

cluding the fold lines needed to get Fig. 1.

To be able to draw Fig. 1 we have to get the

value of H, the distance between two opposite faces of

an octahedron (see Fig. 2).

Fig. 4 is a view of the tetrahedron before its

vertices have been flattened out.