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...

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...

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

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...

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

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

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...

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...

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

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...

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...

truncation. The resulting polyhedron has 4 equilateral triangles and 4 regular hexagons, 18 edges, and 12 vertices. A Goldberg polyhedron is one whose faces...

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...

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

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....

In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra. They may be obtained by stellating the regular convex dodecahedron and...

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

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

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...

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...

Wythoff symbol is a notation representing a Wythoff construction of a uniform polyhedron or plane tiling within a Schwarz triangle. It was first used by Coxeter...

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...

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

Trigonal trapezohedron Regular skew polyhedron Waterman polyhedron Wedge Polyhedral compound and Uniform polyhedron compound Compound of cube and octahedron...

In geometry, an octahedron (pl.: octahedra or octahedrons) is a polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid...

anticube. If all its faces are regular, it is a semiregular polyhedron or uniform polyhedron. A nonuniform D4-symmetric variant is the cell of the noble...