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

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...

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...

Regular polyhedron List of regular polytopes Uniform polyhedron Uniform star polyhedron Polyhedral compound Regular star 4-polytope – the ten regular star 4-polytopes...

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...

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

and Coxeter diagram . Nonconvex great rhombicuboctahedron - a uniform star polyhedron, with Schläfli symbol r{4,3/2}, and Coxeter diagram . This disambiguation...

icosidodecahedron Har'El, 1993 Uniform Polyhedron, Mathworld (retrieved 10 June 2016) Coxeter, H.S.M., M.S. Longuet-Higgins and J.C.P Miller, Uniform Polyhedra, Phil...

In geometry, a hemipolyhedron is a uniform star polyhedron some of whose faces pass through its center. These "hemi" faces lie parallel to the faces of...

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

quasitruncated square, inverted as {4/3}, is an octagram, t{4/3}={8/3}. The uniform star polyhedron stellated truncated hexahedron, t'{4,3}=t{4/3,3} has octagram faces...

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

This is an indexed list of the uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger. The book was written as a guide book...

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

regular polyhedron is a polyhedron with regular and congruent polygons as faces. Its symmetry group acts transitively on its flags. A regular polyhedron is...

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

star Pentagramma mirificum Regular star 4-polytope Rub el Hizb Star (glyph) Star polyhedron, Kepler–Poinsot polyhedron, and uniform star polyhedron Starfish...

geometry, the great complex icosidodecahedron is a degenerate uniform star polyhedron. It has 12 vertices, and 60 (doubled) edges, and 32 faces, 12 pentagrams...

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...

In geometry, the great icosidodecahedron is a nonconvex uniform polyhedron, indexed as U54. It has 32 faces (20 triangles and 12 pentagrams), 60 edges...

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

icosidodecahedron Snub dodecahedron Prismatic uniform polyhedron Prism Antiprism Uniform star polyhedron Cubitruncated cuboctahedron Cubohemioctahedron...

icosidodecahedron) is a uniform star polyhedron, indexed as U69. It is given a Schläfli symbol sr{5⁄3,3}, and Coxeter-Dynkin diagram . In the book Polyhedron Models by...

(or quasitruncated hexahedron, and stellatruncated cube) is a uniform star polyhedron, indexed as U19. It has 14 faces (8 triangles and 6 octagrams)...

icosicosidodecahedron, or retroholosnub icosahedron) is a nonconvex uniform polyhedron, indexed as U72. It has 112 faces (100 triangles and 12 pentagrams)...

complex icosidodecahedron is a degenerate uniform star polyhedron. Its edges are doubled, making it degenerate. The star has 32 faces (20 triangles and 12 pentagons)...

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

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