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The kissing number of a sphere is 12. This led Fejes Tóth (1943) to conjecture that in any unit sphere packing, the volume of any Voronoi cell around any sphere is at least ...
A proposition which is consistent with known data, but has neither been verified nor shown to be false. It is synonymous with hypothesis.
The dodecahedral graph is the Platonic graph corresponding to the connectivity of the vertices of a dodecahedron, illustrated above in four embeddings. The left embedding ...
A figurate number which is constructed as a centered cube with a square pyramid appended to each face, RhoDod_n = CCub_n+6P_(n-1)^((4)) (1) = (2n-1)(2n^2-2n+1), (2) where ...
The rhombic dodecahedral graph is the Archimedean dual graph which is the skeleton of the rhombic dodecahedron (as well as the Bilinski dodecahedron). It is the Levi graph of ...
The snub dodecahedral graph is a quintic graph on 60 nodes and 150 edges that corresponds to the skeleton of the snub dodecahedron, great inverted snub icosidodecahedron, ...
The disdyakis dodecahedral graph is Archimedean dual graph which is the skeleton of the disdyakis dodecahedron. It is implemented in the Wolfram Language as ...
The pentakis dodecahedral graph is Archimedean dual graph which is the skeleton of the disdyakis triacontahedron. It is implemented in the Wolfram Language as ...
The cubic Archimedean graph on 60 nodes and 90 edges that is the skeleton of the truncated dodecahedron. It is implemented in the Wolfram Language as ...
The truncated great dodecahedral graph is the skeleton of the small stellated truncated dodecahedron and truncated great dodecahedron. It is illustrated above in a number of ...
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