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...

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

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

such it is one of the Archimedean solids and more particularly, a quasiregular polyhedron. An icosidodecahedron has icosahedral symmetry, and its first stellation...

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...

alternately colored triangles on a sphere. Polyhedron Regular polyhedron Quasiregular polyhedron Semiregular polyhedron List of uniform polyhedra List of uniform...

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

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

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

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...

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...

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

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...

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

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...

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

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

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

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

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

order 1296. It has a half-symmetry quasiregular construction as , as a rectification of the Hessian polyhedron, . Along with the semiregular polytope...

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

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

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...

In geometry, an octahedron (pl.: octahedra or octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron...

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

or alternated cubic honeycomb (Simple tetroctahedric check), ↔ (Also quasiregular polytope) Gyrated alternated cubic honeycomb (Complex tetroctahedric...