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The Cayley-Menger determinant is a determinant that gives the volume of a simplex in j dimensions. If S is a j-simplex in R^n with vertices v_1,...,v_(j+1) and B=(beta_(ik)) ...

In plane geometry, a chord is the line segment joining two points on a curve. The term is often used to describe a line segment whose ends lie on a circle. The term is also ...

Combinatorial geometry is a blending of principles from the areas of combinatorics and geometry. It deals with combinations and arrangements of geometric objects and with ...

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 ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...

A number of attractive cube 10-compounds can be constructed. The first can be obtained by beginning with an initial cube and rotating it by an angle theta=sin^(-1)(sqrt(3/8)) ...

A deltahedron is a polyhedron whose faces are congruent equilateral triangles (Wells 1986, p. 73). Note that polyhedra whose faces could be triangulated so as to be composed ...

A dipyramid, also called a bipyramid, consists of two pyramids symmetrically placed base-to-base. The dipyramids are duals of the regular prisms. Their skeletons are the ...

The dodecadodecahedron is the uniform polyhedron with Maeder index 36 (Maeder 1997), Wenninger index 73 (Wenninger 1989), Coxeter index 45 (Coxeter et al. 1954), and Har'El ...

The elongated square gyrobicupola nonuniform polyhedron obtained by rotating the bottom third of a small rhombicuboctahedron (Ball and Coxeter 1987, p. 137). It is also ...