MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

• Joining the extremities of the small crosses and its center B to the vertices of the mentioned
  cube, we get the macle as can be seen in Figs. 3 or 4.


• In both Figs. 3 and 4 we can observe the shaded pentagonal faces forming both dodecahe-
  dra, direct and inverse.

Fig. 5 is the folding diagram pertaining to one of the 6 bodies to be attached to the re-

spective faces of the cube already mentioned.

Every triangle in Fig. 5 is determined:

CA = CD = l, is the side of the original polyhedron.

AD = 1,618034 l, is the facial pentagon ́s diagonal: it will be the side of the starting

cube to be previously constructed.

CB = l / 2

AB = 1,248606 l (GI of Point 18.6.1; see also DB in Fig. 3).

To finish, we must insist that to materialise the Iron Cross, the starting polyhedron we

want is a cube with faces CDCD rather than a dodecahedron.

5

A

D C

B

B B

C B

C

C

Interlude