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Let a group G have a group presentation G=<x_1,...,x_n|r_j(x_1,...,x_n),j in J> so that G=F/R, where F is the free group with basis {x_1,...,x_n} and R is the normal subgroup ...

Let a chess piece make a tour on an n×n chessboard whose squares are numbered from 1 to n^2 along the path of the chess piece. Then the tour is called a magic tour if the ...

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 ...

The cubitruncated cuboctahedron (called the cubotruncated cuboctahedron by Wenninger 1971, p. 121) is the uniform polyhedron with Maeder index 16 (Maeder 1997), Wenninger ...

The great dodecahemidodecahedron is the uniform polyhedron with Maeder index 70 (Maeder 1997), Wenninger index 107 (Wenninger 1989), Coxeter index 86 (Coxeter et al. 1954), ...

The hemicube, which might also be called the square hemiprism, is a simple solid that serves as an example of one of the two topological classes of convex hexahedron having 7 ...

When the elongated square pyramid with unit edge lengths (i.e., an equilateral obelisk) is truncated by a plane passing through opposite corners of its square base and the ...

In determinant expansion by minors, the minimal number of transpositions of adjacent columns in a square matrix needed to turn the matrix representing a permutation of ...

A first compound of 20 octahedra can be constructed from the vertices of icositruncated dodecadodecahedron uniform polyhedron and a second from the vertices of the great ...

The Szilassi polyhedron is a heptahedron that is topologically equivalent to a torus and for which every pair of faces has a polygon edge in common. The Szilassi polyhedron ...