classified in parallel with their dual (uniform) polyhedron. The dual of a regular polyhedron is regular, while the dual of an Archimedean solid is a Catalan...

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, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges...

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

list of the thirteen solids in 1865. In general, each face of a dual uniform polyhedron (including the Catalan solid) can be constructed by using the Dorman...

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:...

icosahedron. The dual polyhedron of the small triambic icosahedron is the small ditrigonal icosidodecahedron. As this is a uniform polyhedron, the small triambic...

duality, vertex figures, surface area, volume, interior lines, Dehn invariant, and symmetry. A symmetry of a polyhedron means that the polyhedron's appearance...

dimensions. A dual compound is composed of a polyhedron and its dual, arranged reciprocally about a common midsphere, such that the edge of one polyhedron intersects...

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...

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

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

sides, six vertices at which four sides meet, and twelve edges. Its dual polyhedron is a cube. It can be formed as the convex hull of the six axis-parallel...

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

are self-dual. Wikimedia Commons has media related to Honeycombs (geometry). List of uniform tilings Regular honeycombs Infinite skew polyhedron Plesiohedron...

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

popular spherical polyhedron is the beach ball, thought of as a hosohedron. Some "improper" polyhedra, such as hosohedra and their duals, dihedra, exist...

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...

great rhombicuboctahedron, which is not a uniform polyhedron. The great deltoidal icositetrahedron is the dual of the nonconvex great rhombicuboctahedron...

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...

vertex figure is denoted as 3 ⋅ 6 2 {\displaystyle 3\cdot 6^{2}} . Its dual polyhedron is triakis tetrahedron, a Catalan solid, shares the same symmetry as...

the term 'dual' covers both kinds. The dual of a noble polyhedron is also noble. Many are also self-dual: The five regular polyhedra form dual pairs, with...

isometries preserving the polyhedron or tiling. All regular polygons, apeirogons and regular star polygons are isogonal. The dual of an isogonal polygon...

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

configuration. An isohedron has an even number of faces. The dual of an isohedral polyhedron is vertex-transitive, i.e. isogonal. The Catalan solids, the...

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

antipodal map. It is the only uniform (traditional) polyhedron that is projective – that is, the only uniform projective polyhedron that immerses in Euclidean...