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By the duality principle, for every polyhedron, there exists another polyhedron in which faces and polyhedron vertices occupy complementary locations. This polyhedron is ...

The dodecadodecahedral graph is the skeleton of the dodecadodecahedron, great dodecahemicosahedron, and small dodecahemicosahedron. It is illustrated above in several ...

Is it possible to cover completely the surface of a sphere with congruent, nonoverlapping arcs of great circles? Conway and Croft (1964) proved that it can be covered with ...

The Archimedean duals are the 13 duals of the 13 Archimedean solids, sometimes called the Catalan solids. They are summarized in the following table and illustrated below ...

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 ...

The dual polyhedra of the Archimedean solids, given in the following table. They are known as Catalan solids in honor of the Belgian mathematician who first published them in ...

The uniform polyhedra are polyhedra consisting of regular (possibly polygrammic) faces of equal edge length whose polyhedron vertices are all symmetrically equivalent. The ...

The term "rhombicuboctahedron" is most commonly used (e.g., Wenninger 1989, p. 27; Maeder 1997) to refer to the 26-faced Archimedean solid with faces 8{3}+18{4}. Cundy and ...

Elliptic geometry is a non-Euclidean geometry with positive curvature which replaces the parallel postulate with the statement "through any point in the plane, there exist no ...

A spheric section is the curve formed by the intersection of a plane with a sphere. Excluding the degenerate cases of the plane tangent to the sphere or the plane not ...