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...

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

In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-)  'many' and ἕδρον (-hedron)  'base, seat') is a three-dimensional figure...

In geometry, a uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i...

A dual uniform polyhedron is the dual of a uniform polyhedron. Where a uniform polyhedron is vertex-transitive, a dual uniform polyhedron is face-transitive...

bipyramid, Octagonal bipyramid, Decagonal bipyramid Trapezohedron Uniform star polyhedron Cubitruncated cuboctahedron Cubohemioctahedron Ditrigonal dodecadodecahedron...

all regular, the hexagonal prism is a semiregular polyhedron, more generally, a uniform polyhedron, and the fourth in an infinite set of prisms formed...

all regular, the pentagonal prism is a semiregular polyhedron, more generally, a uniform polyhedron, and the third in an infinite set of prisms formed...

prismatic uniform polyhedron is a uniform polyhedron with dihedral symmetry. They exist in two infinite families, the uniform prisms and the uniform antiprisms...

geometry, a uniform polyhedron compound is a polyhedral compound whose constituents are identical (although possibly enantiomorphous) uniform polyhedra...

In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality. There are two general...

quasiregular polyhedron is a uniform polyhedron which has just two kinds of face alternating around each vertex. A regular polyhedron is a uniform polyhedron which...

triangular prism may be both semiregular and uniform. The triangular prism can be used in constructing another polyhedron. Examples are some of the Johnson solids...

Skilling's figure, is a degenerate uniform star polyhedron. It was proven in 1970 that there are only 75 uniform polyhedra other than the infinite families...

mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling. It is often referred to as Wythoff's kaleidoscopic...

canonical dual compound. For a uniform polyhedron, each face of the dual polyhedron may be derived from the original polyhedron's corresponding vertex figure...

In geometry, the tetrahemihexahedron or hemicuboctahedron is a uniform star polyhedron, indexed as U4. It has 7 faces (4 triangles and 3 squares), 12...

uniform truncation, a truncation operator applied to a regular polyhedron (or regular polytope) which creates a resulting uniform polyhedron (uniform...

Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-7 to 3-9) Weisstein, Eric W. "Uniform Polyhedron". MathWorld....

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive...

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...

An isogonal polyhedron and 2D tiling has a single kind of vertex. An isogonal polyhedron with all regular faces is also a uniform polyhedron and can be...

In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy (rigidly moved without rotation) of the...

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 spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded...

and the three-dimensional analogue is a polyhedron. Topologically 4-polytopes are closely related to the uniform honeycombs, such as the cubic honeycomb...

geometry, the nonconvex great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U67. It has 62 faces (20 triangles, 30 squares and 12...

tessellate space alongside other uniform prisms, has 14 faces. The Szilassi polyhedron and its dual, the Császár polyhedron, are the simplest toroidal polyhedra;...

In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol {5⁄2,5}. It is one of four...

(dṓdeka) 'twelve' and ἕδρα (hédra) 'base, seat, face') or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular...