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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...

uniform polyhedra Prince Rupert's cube#Generalizations Quasicrystal Regular polyhedron Semiregular polyhedron Toroidal polyhedron Uniform polyhedron Steckles...

all regular, the hexagonal prism is a semiregular polyhedron, more generally, a uniform polyhedron, and the fourth 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...

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

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

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...

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

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...

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

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...

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...

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...

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

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

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