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Let a discrete distribution have probability function p_k, and let a second discrete distribution have probability function q_k. Then the relative entropy of p with respect ...

Measurements of a centered convex body in Euclidean n-space (for n>=3) show that its brightness function (the volume of each projection) is smaller than that of another such ...

A stereohedron is a convex polyhedron that is isohedrally space-filling, meaning the symmetries of a tiling of copies of a stereohedron take any copy to any other copy. The ...

Triangle picking is the process of picking triangles at random within a given shape in the plane, in space, or in a higher dimension. The most natural definition of a random ...

The equilateral triaugmented triangular prism is the Johnson solid J_(51) constructed by erecting a regular tetrahedron on each square face of an equilateral triangular ...

The tetragonal antiwedge is the topological class of hexahedron. It has 10 edges and 6 vertices and its faces consist of 4 triangles and 2 quadrilaterals. A tetragonal ...

The trapezo-rhombic dodecahedron, also called the rhombo-trapezoidal dodecahedron, is a general dodecahedron consisting of six identical rhombi and six identical isosceles ...

Fuglede (1974) conjectured that a domain Omega admits an operator spectrum iff it is possible to tile R^d by a family of translates of Omega. Fuglede proved the conjecture in ...

The geometric span is largest possible distance between two points drawn from a finite set of points. It is therefore closely related to the generalized diameter of a closed ...

A number of attractive polyhedron compounds consisting of three octahedra. The first (left figues) is the polyhedron dual of the cube 3-compound. These compounds will be ...