Search Results for ""

The term "square" can be used to mean either a square number ("x^2 is the square of x") or a geometric figure consisting of a convex quadrilateral with sides of equal length ...

Expansion is an affine transformation (sometimes called an enlargement or dilation) in which the scale is increased. It is the opposite of a geometric contraction, and is ...

A compound of five regular dodecahedra with the symmetry of the icosahedron (Wenninger 1983, pp. 145-147) can be constructed by taking a dodecahedron with top and bottom ...

A number of four-tetrahedron compounds can be constructed by rotating about the center-centroid lines of each face. Three such compounds are shown above for rotations by ...

The great ditrigonal dodecicosidodecahedron is the uniform polyhedron with Maeder index 42 (Maeder 1997), Wenninger index 81 (Wenninger 1989), Coxeter index 54 (Coxeter et ...

There are a number of attractive polyhedron compounds of two cubes. The first (left figures) is obtained by allowing two cubes to share opposite polyhedron vertices then ...

The mean tetrahedron volume of a tetrahedron with vertices chosen at random inside another tetrahedron of unit volume is given by V^_ = (13)/(720)-(pi^2)/(15015) (1) = ...

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 (small) rhombicuboctahedron (Cundy and Rowlett 1989, p. 105), sometimes simply called the rhombicuboctahedron (Wenninger 1989, p. 27; Maeder 1997, Conway et al. 1999), is ...

An n-trapezohedron, also called an antidipyramid, antibipyramid, or deltohedron (not to be confused with a deltahedron), is a solid composed of interleaved symmetric ...