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The gyroelongated pentagonal pyramid is Johnson solid J_(11) and can be obtained by cumulating the top of a pentagonal antiprism, or alternately by replacing one pentagonal ...

Define a carefree couple as a pair of positive integers (a,b) such that a and b are relatively prime (i.e., GCD(a,b)=1) and a is squarefree. Similarly, define a strongly ...

If a Sylow 2-subgroup T of G lies in a unique maximal 2-local P of G, then P is a "strongly embedded" subgroup of G, and G is known.

Intuitively, a model of d-dimensional percolation theory is said to be a Bernoulli model if the open/closed status of an area is completely random. In particular, it makes ...

The small triambic icosahedron is the dual polyhedron of the small ditrigonal icosidodecahedron with Maeder index 30 (Maeder 1997), Weinninger index 70 (Wenninger 1971, p. ...

Geometry

Due to nonlinearities in weather processes, a butterfly flapping its wings in Tahiti can, in theory, produce a tornado in Kansas. This strong dependence of outcomes on very ...

700 The great dodecahemicosahedron is the uniform polyhedron with Maeder index 65 (Maeder 1997), Wenninger index 102 (Wenninger 1989), Coxeter index 81 (Coxeter et al. 1954), ...

The great icosihemidodecahedron is the uniform polyhedron with Maeder index 71 (Maeder 1997), Wenninger index 106 (Wenninger 1989), Coxeter index 85 (Coxeter et al. 1954), ...

A presentation of a group is a description of a set I and a subset R of the free group F(I) generated by I, written <(x_i)_(i in I)|(r)_(r in R)>, where r=1 (the identity ...