Topologically equivalent to a torus; it demonstrates that seven colors are necessary for a map on a surface topologically equivalent to a torus. The tetrahedron otoh shows 4 are necessary for a map on a surface equivalent to a sphere.
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If one uses Euler's formula for polyhedrons: f + v - e = 2 - 2*h (f: faces, v: vertices, e: edges, h: holes) and solves for "each face shares an edge with every other face", one gets: h = (f - 4) * (f - 3) / 12 f=4 is the tetrahedron; f=7, the Szilassi polyhedron...
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The next solution for f that gives a whole number solution is 12. This would give a polyhedron with 12 faces, 66 edges, 44 vertices, and 6 holes. It is not clear if such an object can even be realized geometrically (might be "abstract"). Higher solutions are even hairer.
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Now I want a building made out of it
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You have a name that could really suit a high rise too! So I would suggest naming it after you. :D
Kraj razgovora
Novi razgovor -
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Hvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi
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At first I thought this was a 3D tiling but then realized not all the shapes are the same.
Hvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi
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Čini se da učitavanje traje već neko vrijeme.
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