MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández

two faces 3. What is peculiar now, though, is that the two faces 1 are different to each other,

and the same applies to faces 2 and 3. Hence, now we have 6 different faces instead of the

three we had before. We still have a tri-hexa-flexagon, though. All this can be seen in Fig. 9

which, when unfolded yields Fig. 10 : Both figures evoke a kaleidoscopic vision.

Going a bit further we might say that flexagons have to be constructed but not necessar-

ily with straight paper strips, nor even have to be equilateral triangle based.

Fig. 11 (lower side) shows a strip that properly folded will yield an hexa-hexa-flexagon:

a hexagonal based flexagon with the possibility of six faces. The upper illustration is the

base for another different flexagon. Hence, tri, hexa, octo ... n-hexa-flexagons, can be con-

structed, though paper accumulation handicaps flexibility.

Looking at Figs. 8 and 10 we can see how difficult may be to define the fold lines and

its nature (mountain or valley) in order that the final result will be the wished hexagon (in

any case gluing the triangles of both extremities). A. Stone and P. Jackson have developed

X

3

2

1

Y

3

2

1

B

2

(^21)
1
3
3
3
(^32)
1
2 1
CA
10
11
9
3
3
2
1
1
1
1
1
1
1
1
1
(^11)
1
3
3
3
3
2
2
2
2
(^2333)
(^333)
2
2
2
2
2
2