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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 ...

Hex is a two-player game invented by Piet Hein in 1942 while a student at Niels Bohr's Institute for Theoretical Physics, and subsequently and independently by John Nash in ...

There are at least three definitions of "groupoid" currently in use. The first type of groupoid is an algebraic structure on a set with a binary operator. The only ...

The Paulus graphs are the 15 strongly regular graphs on 25 nodes with parameters (nu,k,lambda,mu)=(25,12,5,6) and the 10 strongly regular graphs on 26 nodes with parameters ...

A rigorous mathematical argument which unequivocally demonstrates the truth of a given proposition. A mathematical statement that has been proven is called a theorem. ...

A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...

The Klein bottle is a closed nonorientable surface of Euler characteristic 0 (Dodson and Parker 1997, p. 125) that has no inside or outside, originally described by Felix ...

The number of colors sufficient for map coloring on a surface of genus g is given by the Heawood conjecture, chi(g)=|_1/2(7+sqrt(48g+1))_|, where |_x_| is the floor function. ...

Let a closed interval [a,b] be partitioned by points a<x_1<x_2<...<x_(n-1)<b, where the lengths of the resulting intervals between the points are denoted Deltax_1, Deltax_2, ...

A kit consisting of colored rods and slotted balls that can be used to construct three-dimensional configurations. The balls into which the rods are placed resemble an ...