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...

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

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...

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

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

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...

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, a quasiregular polyhedron is a uniform polyhedron that has exactly two kinds of regular faces, which alternate around each vertex. They are...

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

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...

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

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...

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

Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons. They are sometimes defined to exclude the uniform polyhedrons. There are ninety-two...

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

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

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...

that each polyhedron can be sent to any of the others, as in uniform compounds), then if H is the stabilizer of a single chosen polyhedron, the polyhedra...

the octahemioctahedron or allelotetratetrahedron is a nonconvex uniform polyhedron, indexed as U3. It has 12 faces (8 triangles and 4 hexagons), 24 edges...

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...

was truncated. As a uniform polyhedron that is not a prism or antiprism, this is an Archimedean solid. Gyrobifastigium: Two uniform triangular prisms glued...

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

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...

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...

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....

dirhombicosidodecahedron (or great snub disicosidisdodecahedron) is a nonconvex uniform polyhedron, indexed last as U75. It has 124 faces (40 triangles, 60 squares,...

Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical...