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A real-valued function g defined on a convex subset C subset R^n is said to be quasi-concave if for all real alpha in R, the set {x in C:g(x)>=alpha} is convex. This is ...

Connectivity properties obey the following hierarchy: convex => star convex => pathwise-connected => connected.

Except for convex polygons, every simple polygon has at least one mouth.

The pentagrammic dipyramid is the dual polyhedron of the pentagrammic prism U_(78).

The dual polyhedron of the tetrahemihexahedron U_4 and Wenninger dual W_(67).

A polynomial is called logarithmically concave (or log-concave) if the sequence of its coefficients is logarithmically concave. If P(x) is log-convex and Q(x) is unimodal, ...

A polyhedron compound of the great icosahedron and its dual great stellated dodecahedron most easily constructed by adding the polyhedron vertices of the former to the latter.

A polyhedron consisting of a n-gon, a parallel 2n-gon rotated a half-edge turn, and a band of paired triangles separated by pentagons. The only true member giving a ...

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 cube-octahedron compound is a polyhedron compound composed of a cube and its dual polyhedron, the octahedron. It is implemented in the Wolfram Language as ...