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

mathematics, quasiregular may refer to: Quasiregular element, in the context of ring theory Quasiregular map in analysis Quasiregular polyhedron, in the context...

it is one of the Archimedean solids and more particularly, a quasiregular polyhedron. One way to construct the icosidodecahedron is to start with two...

discarded, either of two hemipolyhedra may be derived from each quasiregular polyhedron, except for the octahedron as a tetratetrahedron, where m = n =...

edges, each separating a triangle from a square. As such, it is a quasiregular polyhedron, i.e., an Archimedean solid that is not only vertex-transitive...

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

(See the Dual polyhedron article.) There are nine convex isotoxal polyhedra: the five (regular) Platonic solids, the two (quasiregular) common cores of...

of prisms and antiprisms, the convex polyhedrons as in 5 Platonic solids and 13 Archimedean solids—2 quasiregular and 11 semiregular— the non-convex star...

polyhedron {2,2}, which is both a hosohedron and a dihedron. All of these have Euler characteristic 2. Quasiregular polyhedron Semiregular polyhedron...

polygon). A quasiregular polyhedron is a uniform polyhedron which has just two kinds of face alternating around each vertex. A regular polyhedron is a uniform...

dimension 2 (a plane tiling) or higher, or a polytope of dimension 3 (a polyhedron) or higher, is isohedral or face-transitive if all its faces are the same...

, and . This alternated construction requires q to be even. A quasiregular polyhedron, with Schläfli symbol { p q } {\displaystyle {\begin{Bmatrix}p\\q\end{Bmatrix}}}...

semiregular polyhedron (or semiregular polytope) is used variously by different authors. In its original definition, it is a polyhedron with regular...

or intersphere of a convex polyhedron is a sphere which is tangent to every edge of the polyhedron. Not every polyhedron has a midsphere, but the uniform...

In geometry, an omnitruncated polyhedron is a truncated quasiregular polyhedron. When they are alternated, they produce the snub polyhedra. All omnitruncated...

polytopes, a complex quasiregular polyhedron can be constructed as a rectification (a complete truncation) of a regular polyhedron. Vertices are created...

In geometry, the Hessian polyhedron is a regular complex polyhedron 3{3}3{3}3, , in C 3 {\displaystyle \mathbb {C} ^{3}} . It has 27 vertices, 72 3{} edges...

rectified 4-polytopes. Dual polytope Quasiregular polyhedron List of regular polytopes Truncation (geometry) Conway polyhedron notation Weisstein, Eric W. "Rectification"...

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 building...

facets: The cuboctahedron, one of two quasiregular polyhedra, has 14 faces and is the only uniform polyhedron with radial equilateral symmetry. The rhombic...

regular honeycomb in Euclidean 3-space, the cubic honeycomb. Two are quasiregular (made from two types of regular cells): The tetrahedral-octahedral honeycomb...

polyhedron is a self-intersecting uniform polyhedron. They are also sometimes called nonconvex polyhedra to imply self-intersecting. Each polyhedron can...

In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries...

non-convex polyhedron is also a non-convex polyhedron. (By contraposition.) There are ten non-convex isotoxal polyhedra based on the quasiregular octahedron...

an alternation of a truncated regular or truncated quasiregular polyhedron. In general a polyhedron can be snubbed if its truncation has only even-sided...

convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. As a Catalan solid, it is the dual polyhedron of the cuboctahedron...

honeycomb, which has eight cubes at each polyhedron vertex. Similarly, in three dimensions there is just one quasiregular honeycomb, which has eight tetrahedra...

truncated icosidodecahedron - the three convex truncated quasiregular polyhedra. The only snub polyhedron with the chiral octahedral group of symmetries is the...

the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of...

(dṓdeka) 'twelve' and ἕδρα (hédra) 'base, seat, face') or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular...