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In 1611, Kepler proposed that close packing (either cubic or hexagonal close packing, both of which have maximum densities of pi/(3sqrt(2)) approx 74.048%) is the densest ...

Two sextuples of skew lines on the general cubic surface such that each line of one is skew to one line in the other set. In all, there are 30 points, with two lines through ...

A zero-symmetric graph is a vertex-transitive cubic graph whose edges are partitioned into three orbits by its automorphism group. The figures above show some small ...

The cubeplex graph is the cubic Hamiltonian graph on 12 nodes illustrated above in several embeddings and corresponding to the graph Gamma_1 in Fischer and Little (2001). It ...

The great rhombicosidodecahedral graph is the Archimedean graph on 120 vertices and 180 edges that is the skeleton of the great rhombicosidodecahedron as well as the uniform ...

The Loupekine snarks are the two snarks on 22 vertices and 33 edges illustrated above. They are implemented in the Wolfram Language as GraphData["LoupekineSnark1"] and ...

The truncated octahedral graph is the cubic Archimedean graph on 24 nodes and 36 edges that is the skeleton of the truncated octahedron. It is isomorphic to the Bruhat graph ...

The Wagner graph is a name sometimes given to the 4-Möbius ladder (Bondy and Murty 2008, pp. 275-276). The association arises through the theorem of Wagner (1937) that graphs ...

Barnette's conjecture asserts that every 3-connected bipartite cubic planar graph is Hamiltonian. The only graph on nine or fewer vertices satisfying Barnette's conditions is ...

An xyz embedding, also called an "xyz drawing," is a three-dimensional embedding such that every axis-parallel line contains either zero or two vertices. Such an embedding is ...