MATHEMATICS AND ORIGAMI

Mathematics and Origami

Skeletonlike TETRAHEDRON

It is made out of 4 corners as vertices (Fig. 5) and 6 cardboard rails as sides (Fig. 6); rail

ends, to 60º.

18.8 CUBE
C = 6 ; V = 8 ; A = 12
Perhaps it is the cube (or hexahedron) the polyhedron that has inspired more paper-
folded solutions, both in quantity and originality. Now we shall outline only some simple
though singular creations and shall also focus on some cubic questions specially related to
mathematics.

18.8.1 Ex-rectangle CUBE

We start with a folding diagram like that in Fig. 1 and end up with the cube of Fig. 2

fully closed on itself.

5

6

O

C D

h

The resultant tetrahedron will show only verti-

ces and sides (Fig. 7) and has to be fixed by gluing or

by sticking paper.

The relation between Figs. 5 and 6 is this: if l

is the side of the triangle with center O, it will be:

3

l

CD=h=

We can assign any length to the rails (of

course, the same for the six) as long as we get the

right proportion in the tetrahedron.

The rails opening to assembly will be fixed to

the dihedral angle of the tetrahedron ́s faces (α angle

in Point 18.2.1)

1