Smooth Full Color Nylon 12 (MJF)
Szilassi polyhedron (smooth)
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Product Description
Each face of this polyhedron shares an edge with each other face.
As a result, it requires seven colours to colour all adjacent faces. This example shows that, on surfaces topologically equivalent to a torus, some subdivisions require seven colors, providing the lower bound for the seven colour theorem.
It is the polyhedric version of the seven colors map on a torus.
https://en.wikipedia.org/wiki/Four_color_theorem#/media/File:Projection_color_torus.png
https://en.wikipedia.org/wiki/File:Heawood_graph_on_torus.webm
It can be checked that the Euler's characterisitc is 0 (like a torus) with 21 edges, 14 vertices and 7 faces (heptahedron).
The tetrahedron and the Szilassi polyhedron are the only two known polyhedra in which each face shares an edge with each other face.
As a result, it requires seven colours to colour all adjacent faces. This example shows that, on surfaces topologically equivalent to a torus, some subdivisions require seven colors, providing the lower bound for the seven colour theorem.
It is the polyhedric version of the seven colors map on a torus.
https://en.wikipedia.org/wiki/Four_color_theorem#/media/File:Projection_color_torus.png
https://en.wikipedia.org/wiki/File:Heawood_graph_on_torus.webm
It can be checked that the Euler's characterisitc is 0 (like a torus) with 21 edges, 14 vertices and 7 faces (heptahedron).
The tetrahedron and the Szilassi polyhedron are the only two known polyhedra in which each face shares an edge with each other face.
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