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A polyhedron in a hyperbolic geometry.

Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...

Any four mutually tangent spheres determine six points of tangency. A pair of tangencies (t_i,t_j) is said to be opposite if the two spheres determining t_i are distinct from ...

In two dimensions, there are two periodic circle packings for identical circles: square lattice and hexagonal lattice. In 1940, Fejes Tóth proved that the hexagonal lattice ...

An isohedron is a convex polyhedron with symmetries acting transitively on its faces with respect to the center of gravity. Every isohedron has an even number of faces ...

An equilateral zonohedron is a zonohedron in which the line segments of the star on which it is based are of equal length (Coxeter 1973, p. 29). Plate II (following p. 32 of ...

The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...

The hundred-dollar, hundred-digits challenge problems are a set of ten problems in numerical analysis published in the January/February 2002 issue of SIAM News ...

The map x_(n+1)=2mux_n, (1) where x is computed modulo 1. A generalized Baker's map can be defined as x_(n+1) = {lambda_ax_n y_n<alpha ; (1-lambda_b)+lambda_bx_n y_n>alpha ...

A box integral for dimension n with parameters q and s is defined as the expectation of distance from a fixed point q of a point r chosen at random over the unit n-cube, ...