Let's draw
several regular polygons, i.e. a triangle, a square, a pentagon
and a hexagon… These flat figures can constitute five absolutely
symmetrical volumetric bodies (Archimedean bodies). They are:
tetrahedron that consists of four regular triangles, cube with
six square sides, octahedron made of eight triangles, dodecahedron
with twelve pentagonal sides and ecosahedron made from twenty
regular triangles. What will happen if we decide to work not with
flat surfaces but with outlines of regular triangles? It is a
common knowledge that a line has only one dimension, i.e. its
length. Hence, you cannot lift it up. But you can use a thin strip
of paper as a model. You will see that four regular triangles
made from this strip of paper interweave in a correct manner.
Besides, than that, if this strip of paper is of a correct width,
you will get a very attractive paper structure. We wrote about
it in the issue N 2, 1996 (Michalkinski's puzzles. Four Interweaved
Triangles). Another curious construction comes from four interweaved
hexagons also made from a strip of paper. Let's see how we can
achieve this effect in practice.

V. Michalkinski
