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

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

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

be quasiregular, although they have regular faces, and its dual is face-transitive and edge-transitive. A vertex- but not edge-transitive polyhedron with...

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...

(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...

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

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

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

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

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

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...

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

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...

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...

called trigonal antiprism. Therefore, it has the property of quasiregular, a polyhedron in which two different polygonal faces are alternating and meet...

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

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

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

a rectified cube or rectified octahedron, and one of only two convex quasiregular polyhedra. It contains eight equilateral triangular faces, whose first...

edge-transitive polyhedron has the same value. This includes the 5 Platonic solids, the 13 Catalan solids, the 4 Kepler–Poinsot polyhedra, the two quasiregular solids...

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

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....

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...

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...

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