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

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...

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

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...

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

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...

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

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

, 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...

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

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...

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...

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

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"...

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...

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

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...

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...

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

band model The triheptagonal tiling can be seen in a sequence of quasiregular polyhedrons and tilings: From a Wythoff construction there are eight hyperbolic...

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

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

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...

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....

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