MATHEMATICS AND ORIGAMI

Mathematics and Origami

a rather elaborate graphical process to enable the adequate folding of a given strip.

For the moment we should forget the combinatorial calculus to get the formulas leading

to a flexagon mathematical approach: Mathematicians have not yet arrived to define con-

clusions because of the great number of restrains associated to that constructive process.

As we mentioned before, the equilateral triangles that are the base for hexaflexagons,

may be superseded by squares to produce tetraflexagons. Moreover, flexagons have to be

not necessarily plane as those seen hereby: they can be solid, too.

These employ the same raw material than the others, i.e., equilateral triangles or

squares that eventually configure in combinations of cubes, parallelepipeds or tetrahedrons

instead of polygons.

Once we are about jumping from 2 to 3D, we shall exhibit a solid flexagon. These op-

tions, as well as open flexagons (enchained rectangles alike folding screens) hold off the

initial conception of a strip glued at its extremities.

The one shown in Figs. 12 to 17 is original of R. Neal. Fig. 12 is the starting plan view

with the necessary folds to get Fig. 13. From this, and forcing downwards its base on the

center, we get the total flattening of the figure with the four faces 1 as shown in Fig. 14.

These faces are indicated in Fig. 12 on their respective places: A1 for the obverse and R1

for the reverse.

The rest of forms are some of the possible resultant figures after manipulating the for-

mer.

12

A1 R1

R1 A1

13

(^11)
(^11)
14
17