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A convex polyhedron is defined as the set of solutions to a system of linear inequalities mx<=b (i.e., a matrix inequality), where m is a real s×d matrix and b is a real ...

There are a number of attractive compounds of two regular tetrahedra. The most symmetrical is the arrangement whose outer hull is the stella octangula (left figure), while ...

The happy end problem, also called the "happy ending problem," is the problem of determining for n>=3 the smallest number of points g(n) in general position in the plane ...

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.

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, ...

The Platonic solids, also called the regular solids or regular polyhedra, are convex polyhedra with equivalent faces composed of congruent convex regular polygons. There are ...

A plane figure consisting of four points, each of which is joined to two other points by a line segment (where the line segments may intersect). A quadrangle may therefore be ...

Each centered convex body of sufficiently high dimension has an "almost spherical" k-dimensional central section.