MATHEMATICS AND ORIGAMI

Mathematics and Origami

As we can note, the auxiliary dodecahedron has enable us to draw Figs. 1, 2, 3, 4 but it
does not allow the materialisation of the stellate polyhedron because of the above mentioned
interference.

Fig. 5 is the folding diagram for the polyhedral angle in H (only the lateral closing lap
joint is shown). Segments type DC are kept as an indication of the stellate pentagons pertaining
to the auxiliary dodecahedron. While assembling the 12 elements to Fig. 5, all the dihedral an-
gles will appear automatically. Fig. 6 is the finished stellate polyhedron.

This polyhedron has 12 Vertices (V = 12), one for each face of the auxiliary dodecahe-
dron: all of them are stellate polyhedral angles; moreover, they are pentagonal, i.e. with E = 2
(a stallate pentagon has also species 2).
Out of each vertex start 5 sides making a total of 5 × 12 = 60 ; but since each side is

common to 2 vertices, we ́ll have: 30
2

60

A= = ; 30 sides in the end.

F

3

O

H

D E

O ́

H ́

H

D

F

C

4

5

D

C

F

H