Copyright Peter Raedschelders

 

Snake

In mathematics, the best known solids are the 5 Platonic solids: tetrahedron,octahedron, cube, isocahedron and dodecahedron. These are regular solids constructed with only one sort of polygons. So is the cube constructed with 6 squares (4), the dodecahedron with 12 pentagons (5) .

Another sort of solids are the 13 Archimedean solids with names as cuboctahedron and isosidodecahedron. These are solids constructed with more the one sort of regular polygons. The best known is a football which is constructed with regular pentagons (5) surrounded with regular hexagons (6).

Is it known that a solids with pentagons (7) together with other regular polygons is impossible, but nevertheless we tried to construct one. The results is a solid with a regular pentagon (7), surrounded with pentagons (5) and "squares". However if we look closely, one can see that the pentagons (5) are not regular (since the angles are not always the same neither are the lengths of the sides). The same is true for the squares, they only look like squares. Only the pentagons (7) are regular.

A snake moves around through the solid and passes through every polygon.

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