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A number of attractive tetrahedron 6-compounds can be constructed. The first compound (left figures) is obtained by combining three stella octangula. A second can be obtained ...

Let G be a planar graph whose vertices have been properly colored and suppose v in V(G) is colored C_1. Define the C_1C_2-Kempe chain containing v to be the maximal connected ...

There are several attractive polyhedron compounds consisting of three cubes. The first (left figures) arises by joining three cubes such that each shares two C_2 axes (Holden ...

Given an undirected graph, a degree sequence is a monotonic nonincreasing sequence of the vertex degrees (valencies) of its graph vertices. The number of degree sequences for ...

The (small) rhombicosidodecahedron (Cundy and Rowlett 1989, p. 111), sometimes simply called the rhombicosidodecahedron (Maeder 1997; Wenninger 1989, p. 27; Conway et al. ...

A number taken to the power 2 is said to be squared, so x^2 is called "x squared." This terminology derives from the fact that the area of a square of edge length x is given ...

The answer to the question "which fits better, a round peg in a square hole, or a square peg in a round hole?" can be interpreted as asking which is larger, the ratio of the ...

The kth power of a graph G is a graph with the same set of vertices as G and an edge between two vertices iff there is a path of length at most k between them (Skiena 1990, ...

A number of the form p^a·A is said to be an antisquare if it fails to be a square number for the two reasons that a is odd and A is a nonsquare (modulo p). The first few ...

The simplest dissection of a square into rectangles of the same areas but different shapes, composed of the seven pieces illustrated above. The square is 210 units on a side, ...