In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling...

In geometry, the Wythoff symbol is a notation representing a Wythoff construction of a uniform polyhedron or plane tiling within a Schwarz triangle. It...

doubled faces produced by Wythoff's construction. Most authors do not allow doubled faces and remove them as part of the construction. Double edges. Skilling's...

wallpaper group p6mm, (*632), and the tiling can be derived as a Wythoff construction within the reflectional fundamental domains of this group. The trihexagonal...

determined, but many can be made as Wythoff constructions from a small set of symmetry groups. These construction operations are represented by the permutations...

on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles...

There are many relationships among the uniform polyhedra. The Wythoff construction is able to construct almost all of the uniform polyhedra from the acute...

Coxeter named this family as δn+1 for an n-dimensional honeycomb. A Wythoff construction is a method for constructing a uniform polyhedron or plane tiling...

of a hexagonal tiling, all generated from reflective symmetry of Wythoff constructions. The (h,k) represent the periodic repeat of one colored tile, counting...

2160-17280 facetted polyzetton (Jonathan Bowers) It is created by a Wythoff construction upon a set of 8 hyperplane mirrors in 8-dimensional space. The 240...

triangular faces. Coxeter defines a quasiregular polyhedron as one having a Wythoff symbol in the form p | q r, and it is regular if q=2 or q=r. The Coxeter-Dynkin...

three dimensions. Uniform honeycombs can be constructed using the Wythoff construction. The Schmitt-Conway biprism is a convex polyhedron with the property...

With orbifold notation symmetry of *n32 all of these tilings are wythoff construction within a fundamental domain of symmetry, with generator points at...

sr{4,4} or s { 4 4 } {\displaystyle s{\begin{Bmatrix}4\\4\end{Bmatrix}}} Wythoff symbol | 4 4 2 Coxeter diagram or Symmetry p4g, [4+,4], (4*2) Rotation...

rr{6,3} or r { 6 3 } {\displaystyle r{\begin{Bmatrix}6\\3\end{Bmatrix}}} Wythoff symbol 3 | 6 2 Coxeter diagram Symmetry p6m, [6,3], (*632) Rotation symmetry...

are shown. The diagonal f-vector numbers are derived through the Wythoff construction, dividing the full group order of a subgroup order by removing one...

allows multiple constructions of the same honeycombs. If cells are colored based on unique positions within each Wythoff construction, these different...

all but one of the uniform polyhedra, through the construction of kaleidoscopes (Wythoff construction). All regular polyhedra, semiregular polyhedra, and...

the 8-dimensional the Euclidean honeycomb, 521. It is created by a Wythoff construction upon a set of 10 hyperplane mirrors in 9-dimensional hyperbolic space...

uniform tilings of the sphere. Most uniform tilings can be made from a Wythoff construction starting with a symmetry group and a singular generator point inside...

tilings. Without right angles in the fundamental triangle, the Wythoff constructions are slightly different. For instance in the (4,3,3) triangle family...

reflective 7-dimensional uniform polytopes are constructed through a Wythoff construction process, and represented by a Coxeter-Dynkin diagram, where each...

Face configuration V4.4.4.4 (or V44) Schläfli symbol(s) {4,4} {∞}×{∞} Wythoff symbol(s) 4 | 2 4 Coxeter diagram(s) Symmetry p4m, [4,4], (*442) Rotation...

circles of the spherical icosahedron used in construction of geodesic domes. It has four Wythoff constructions between four Schwarz triangle families: 2...

a Goursat tetrahedron is a tetrahedral fundamental domain of a Wythoff construction. Each tetrahedral face represents a reflection hyperplane on 3-dimensional...

determined, but most can be made as Wythoff constructions from a small set of symmetry groups. These construction operations are represented by the permutations...

36) Face configuration V6.6.6 (or V63) Schläfli symbol(s) {3,6} {3[3]} Wythoff symbol(s) 6 | 3 2 3 | 3 3 | 3 3 3 Coxeter diagram(s) = Symmetry p6m, [6...

vertices. It is given a Schläfli symbol t0,2{5⁄2,5}, and by the Wythoff construction this polyhedron can also be named a cantellated great dodecahedron...

checkerboard) with Schläfli symbol {4,35,31,1}. The lowest symmetry Wythoff construction has 256 types of facets around each vertex and a prismatic product...

uniform honeycomb Convex uniform honeycombs in hyperbolic space Wythoff construction and Wythoff symbol Hall, Brian C. (2003), Lie Groups, Lie Algebras, and...