In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive—there is an isometry mapping any vertex onto any other. It follows...

A pseudo-uniform polyhedron is a polyhedron which has regular polygons as faces and has the same vertex configuration at all vertices but is not vertex-transitive:...

In geometry, a uniform star polyhedron is a self-intersecting uniform polyhedron. They are also sometimes called nonconvex polyhedra to imply self-intersecting...

figure as the nonconvex great rhombicuboctahedron (a uniform polyhedron), but is not a uniform polyhedron (due to not being isogonal), and has a smaller symmetry...

common). It has the same vertex figure as the pseudo great rhombicuboctahedron, which is not a uniform polyhedron. The great deltoidal icositetrahedron is...

transitive on its vertices; today, this is more commonly referred to as a uniform polyhedron (this follows from Thorold Gosset's 1900 definition of the more general...

a polyhedron constructed by two square cupolas attaching onto the bases of octagonal prism, with one of them rotated. It is a canonical polyhedron. It...

to recover uniformity when changing a spherical polyhedron to its planar counterpart can push faces through the centre of the polyhedron and back out...

operation of alternate truncation of the omnitruncated form. (See Uniform polyhedron#Wythoff construction operators for more details.) Coxeter groups for...

convex uniform honeycomb, being the polygonal surface of a honeycomb with some of the cells removed. Characteristically, an infinite skew polyhedron divides...

dimension 2 (a plane tiling) or higher, or a polytope of dimension 3 (a polyhedron) or higher, is isohedral or face-transitive if all its faces are the same...

icosahedron (/ˌaɪkɒsəˈhiːdrən, -kə-, -koʊ-/ or /aɪˌkɒsəˈhiːdrən/) is a polyhedron with 20 faces. The name comes from Ancient Greek εἴκοσι (eíkosi) 'twenty'...

surface of a polyhedron is called its development. The polyhedron can be thought of as being folded from a sheet of paper (a net for the polyhedron) and it...

deltoidal icositetrahedron, whose dual is the (uniform) rhombicuboctahedron, is tightly related to the pseudo-deltoidal icositetrahedron, whose dual is the...

six octahedra at each polyhedron vertex. However, there are many possible semiregular honeycombs in three dimensions. Uniform honeycombs can be constructed...

Complex number Cartesian coordinate system List of uniform tilings Area 3 dimensions Platonic solid Polyhedron Stereoscopy (3-D imaging) 3-manifold Axis of...

halves can be rotated by 45 degrees to form the pseudo great deltoidal icositetrahedron, analogous to the pseudo-deltoidal icositetrahedron. Faces have three...

whenever they are right pyramids and bipyramids. The Kleetope of a polyhedron is a new polyhedron made by replacing each face of the original with a pyramid,...

across a designated inversion center, which remains fixed. In Euclidean or pseudo-Euclidean spaces, a point reflection is an isometry (preserves distance)...

Orthogonal group Orthogonal matrix Orthogonal polynomials Orthogonal polyhedron Orthogonal trajectory Orthogonalization Gram–Schmidt process Orthonormal...

divided equally between the bonds to the corners of the coordination polyhedron. Starting with Pauling in 1947 a correlation between cation–anion bond...

sphere, with the addition of an internal cavity in the shape of the dual polyhedron of the desired die shape and an internal weight. The weight will settle...

(including the definition in terms of having a finitely-sided fundamental polyhedron) remain equivalent for groups of isometries of hyperbolic n-space where...

is also closely related to the properties of convex bodies. A convex polyhedron is called a zonotope if it is the Minkowski sum of segments. A convex...

Jacopo de Barbari's portrait of Pacioli, painted in 1495; in the truncated polyhedron (and various other mathematical objects) in Albrecht Dürer's engraving...

chained arrow notation, the Conway notation of knot theory, and the Conway polyhedron notation. The Coxeter notation system classifies symmetry groups, describing...

holomorphically convex. D is the union of an increasing sequence of analytic polyhedrons in D. D is pseudoconvex. D is Locally pseudoconvex. The implications...