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Augmentation is the dual operation of truncation which replaces the faces of a polyhedron with pyramids of height h (where h may be positive, zero, or negative) having the ...

There are a number of attractive polyhedron compounds consisting of five cubes. The first of these (left figures) consists of the arrangement of five cubes in the polyhedron ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

The 11-cell is a regular 4-dimensional structure that cannot be represented in 3-dimensional space in any reasonable way and is highly self-intersecting even in 4-dimensional ...

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 coordinates representing any point of an n-dimensional affine space A by an n-tuple of real numbers, thus establishing a one-to-one correspondence between A and R^n. If V ...

In simple terms, let x, y, and z be members of an algebra. Then the algebra is said to be associative if x·(y·z)=(x·y)·z, (1) where · denotes multiplication. More formally, ...

A transformation which transforms from a two-dimensional continuous uniform distribution to a two-dimensional bivariate normal distribution (or complex normal distribution). ...

A real-valued stochastic process {B(t):t>=0} is a Brownian motion which starts at x in R if the following properties are satisfied: 1. B(0)=x. 2. For all times ...

Given a group G, the algebra CG is a vector space CG={suma_ig_i|a_i in C,g_i in G} of finite sums of elements of G, with multiplication defined by g·h=gh, the group ...