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A hexagrammic prism is a prism formed by two regular hexagrams offset along their symmetry axis and with corresponding edges connected by lateral faces. For an equilateral ...

The metabidiminished icosahedron is a convex equilateral solid that is Johnson solid J_(62). The unit metabidiminished icosahedron has volume V=1/6(5+2sqrt(5)) (1) and Dehn ...

A graph G is called d-polytopal if there exists a d-dimensional convex polytope P such that the vertices and edges of G are in a one-to-one incidence-preserving ...

A triacontahedron is a 30-faced polyhedron. Examples include the 14-gonal antiprism, biaugmented truncated cube (Johnson solid J_(67)), 15-gonal dipyramid, 28-gonal prism, ...

A graph corresponding to the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, all of which are regular, planar, polyhedral, and Hamiltonian. The ...

The plastic constant P, sometimes also called le nombre radiant, the minimal Pisot number, plastic number, plastic ratio, platin number, Siegel's number, or silver number, is ...

The small retrosnub icosicosidodecahedron, also called the small inverted retrosnub icosicosidodecahedron, is the uniform polyhedron with Maeder index 72 (Maeder 1997), ...

X is a spherical t-design in E iff it is possible to exactly determine the average value on E of any polynomial f of degree at most t by sampling f at the points of X. In ...

A truncated polyhedron is a polyhedron with truncated faces, given by the Schläfli symbol t{p; q}. The operation implemented as Truncate[polyhedron, r] in the Wolfram ...

A regular graph that is not strongly regular is known as a weakly regular graph. There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n=6, 7, ...