MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

9- To continue with a second module, turn over the strip twice on a pair of succes-

sive diagonals. When constructing the new module we can observe the coinci-

dence of some diagonals of first and second module: glue them to fix the struc-

ture.

10- Turn over again the strip twice to construct a third module. Glue also as before

the coincident diagonals. The obtention of last module requires to double-turn

over the strip, twice.

11- As the process progresses, add new sections to the main strip, to reach the end.

In the meantime we can observe the appearance of the small, hollow pentagons

centered within the pentagonal faces of the polyhedron. Eventually, discard the

left over piece of strip. Fig. 3 shows how the interior of the dodecahedron is put

in shade to avoid the details of inner foldings.

18.11 ICOSAHEDRON

C = 20 ; V = 12 ; A = 30

Begin with an A 4 rectangle (Fig.1) dividing it horizontally in 8 equal parts; discard the

two upper portions. Triangulate according to (Fig.2) discarding also the right hand side shown

in (Fig. 3). Fig. 4 shows, outlined, the 10 triangles forming the icosahedron ́s belt, and, in

shadow, the 5 + 5 triangles that eventually will make up the two opposite domes (recall Point

18.6.2)

Folding to Fig. 5 we get the icosahedron 6 that must be duly fixed.

1 23

✁

4 5