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There are a number of attractive cube 20-compounds that can be constructed by taking the duals of the octahedra in the two octahedron 20-compounds. The second of these was ...

There are a number of attractive cube 25-compounds. One can be constructed from the vertices of the second dodecahedron 6-compound (or second tetrahedron 50-compound) and ...

A cubic triangular number is a positive integer that is simultaneously cubic and triangular. Such a number must therefore satisfy T_n=m^3 for some positive integers n and m, ...

A special case of Stokes' theorem in which F is a vector field and M is an oriented, compact embedded 2-manifold with boundary in R^3, and a generalization of Green's theorem ...

A cyclic graph is a graph containing at least one graph cycle. A graph that is not cyclic is said to be acyclic. A cyclic graph possessing exactly one (undirected, simple) ...

In continuum theory, a dendrite is a locally connected continuum that contains no simple closed curve. A semicircle is therefore a dendrite, while a triangle is not. The term ...

Let a be the angle between v and x, b the angle between v and y, and c the angle between v and z. Then the direction cosines are equivalent to the (x,y,z) coordinates of a ...

The discrete uniform distribution is also known as the "equally likely outcomes" distribution. Letting a set S have N elements, each of them having the same probability, then ...

The dodecahedron-icosahedron compound is a polyhedron compound consisting of a dodecahedron and its dual the icosahedron. In the compound, the dodecahedron and icosahedron ...

A (general) dodecahedron is a polyhedron having 12 faces. Examples include the Bilinski dodecahedron, decagonal prism, elongated square dipyramid (Johnson solid J_(15)), ...