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The 57-cell, also called the pentacontaheptachoron, is a regular self-dual locally projective polytope with 57 hemidodecahedral facets described by Coxeter (1982) and also ...

An aperiodic tiling is a non-periodic tiling in which arbitrarily large periodic patches do not occur. A set of tiles is said to be aperiodic if they can form only ...

The dihedral group D_4 is one of the two non-Abelian groups of the five groups total of group order 8. It is sometimes called the octic group. An example of D_4 is the ...

The disdyakis dodecahedron is the dual polyhedron of the Archimedean great rhombicuboctahedron A_3 and Wenninger dual W_(15). It is also called the hexakis octahedron ...

The disdyakis triacontahedron is the dual polyhedron of the Archimedean great rhombicosidodecahedron A_2. It is also known as the hexakis icosahedron (Holden 1971, p. 55). It ...

A labeling phi of (the vertices) of a graph G with positive integers taken from the set {1,2,...,r} is said to be r-distinguishing if no graph automorphism of G preserves all ...

A compound of five regular dodecahedra with the symmetry of the icosahedron (Wenninger 1983, pp. 145-147) can be constructed by taking a dodecahedron with top and bottom ...

A group action G×X->X is effective if there are no trivial actions. In particular, this means that there is no element of the group (besides the identity element) which does ...

The Einstein field equations are the 16 coupled hyperbolic-elliptic nonlinear partial differential equations that describe the gravitational effects produced by a given mass ...

Elliptic rational functions R_n(xi,x) are a special class of rational functions that have nice properties for approximating other functions over the interval x in [-1,1]. In ...