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Art
Mathematical Art
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Smooth Full Color Nylon 12 (MJF)
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Szilassi polyhedron (smooth)
Made by
MathsBlob
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$
51.06
Full Color Nylon 12 (MJF)
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$ 51.06
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Smooth Full Color Nylon 12 (MJF) - $51.06
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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.
Tags
Heawood
heptahedron
Szilassi polyhedron
torus
Details
What's in the box:
smooth
Dimensions:
4.6 x 5.04 x 6.69 cm
Switch to inches
1.81 x 1.98 x 2.63 inches
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Success Rate:
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Rating:
Mature audiences only.
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MathsBlob
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Rémy Flandin
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