Origami # 1 (11) 1998

Practical Origametry

Michalkinski's molecules

          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.

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Photo of Michalkinski

V. Michalkinski

  Michalkinski's molecules Photo