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The pentagonal icositetrahedron is the 24-faced dual polyhedron of the snub cube A_7 and Wenninger dual W_(17). The mineral cuprite (Cu_2O) forms in pentagonal ...

A perfect cuboid is a cuboid having integer side lengths, integer face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2), (3) and an ...

A polyhedral graph corresponding to the skeleton of a Platonic solid. The five platonic graphs, the tetrahedral graph, cubical graph, octahedral graph, dodecahedral graph, ...

The positive integers 216 and 12960000 appear in an obscure passage in Plato's The Republic. In this passage, Plato alludes to the fact that 216 is equal to 6^3, where 6 is ...

A very general theorem that allows the number of discrete combinatorial objects of a given type to be enumerated (counted) as a function of their "order." The most common ...

A polyhedral nonhamiltonian graph is a graph that is simultaneously polyhedral and nonhamiltonian. The smallest possible number of vertices a nonhamiltonian polyhedral graph ...

Proportionally cutting circles are circles that intersect the sidelines of a reference triangle DeltaABC such that length of the chords that are cut off have lengths mua, ...

A quartic vertex-transitive graph is a quartic graph that is vertex transitive. Read and Wilson (1988, pp. 164-166) enumerate all connected quartic vertex-transitive graphs ...

The quasirhombicosidodecahedron is the uniform polyhedron with Maeder index 67 (Maeder 1997), Wenninger index 105 (Wenninger 1989), Coxeter index 84 (Coxeter et al. 1954), ...

The quasirhombicuboctahedron is the name given by Wenninger (1989, p. 132) to the uniform polyhedron with Maeder index 17 (Maeder 1997), Wenninger index 85 (Wenninger 1989), ...