MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

This indicates that RB, in Fig. 2, is the cube ́s diagonal. From the center of the cube to

its 8 vertices we can adjust 6 quadrangular pyramids like the one seen in Point 18.2.2.1 (lateral

side equal to

2

3

). Two of them are complete (those with the same bases as Fig. 1); the rest are

virtual ones.

The shrinkage produced when passing from Fig. 1 to Fig. 2 is

2

1

. The interference

between the valley-fold diagonals impedes the folding flat of the solid. The 90º twist produced

between figs. 1 and 2 is not docile (bellows-like) but in collapse mode (snap-like).

Let ́s see some variations.

The development of Fig. 4 (gl = 45º; 2 > a > 1; a = 1,2) produces a prismoid with a

natural twist from the right prism. It is docile to an extra twist (total rotation of 69º for Fig. 5).

The final prismoid altitude is h = l = 1

Fig.6 is the development of a prism such that after folding flat produces Fig. 7. The

transition from one to the other takes place in the collapse mode. The collapse is produced

around the center of Fig. 7. After the 90º rotation, upper and lower base coincide.

3

2

1

4

45

1

1,2

(^67)
45
1
1