apeirogonal tiling, the apeirogonal hosohedron, the apeirogonal prism, and the apeirogonal antiprism. Order-3 apeirogonal tiling - hyperbolic tiling Order-4...

In geometry, the order-3 apeirogonal tiling is a regular tiling of the hyperbolic plane. It is represented by the Schläfli symbol {∞,3}, having three regular...

Order-2 apeirogonal tiling, Euclidean tiling of two half-spaces Order-3 apeirogonal tiling, hyperbolic tiling with 3 apeirogons around a vertex Order-4...

The infinite-order apeirogonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {∞,∞}, which means it has countably infinitely...

In geometry, the truncated order-4 apeirogonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{∞,4}. A half symmetry coloring...

geometry, the order-5 apeirogonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {∞,5}. The dual to this tiling represents...

regular tessellation of the Euclidean plane, even when its dual order-2 apeirogonal tiling (infinite dihedron) is. A compound of two "line segment" digons...

geometry, the order-6 apeirogonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {∞,6}. The dual to this tiling represents...

In geometry, the order-4 apeirogonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {∞,4}. This tiling represents the mirror...

truncated order-3 apeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of t{∞,3}. The dual tiling, the infinite-order triakis...

order-3 apeirogonal tiling {∞,3} around each edge. All vertices are ultra-ideal (Existing beyond the ideal boundary) with infinitely many apeirogonal...

tiling facets, with a square pyramid vertex figure. It is similar to the 2D hyperbolic truncated order-4 apeirogonal tiling, t{∞,4}, with apeirogonal...

honeycomb contains that tile 2-hypercycle surfaces, which are similar to the paracompact order-3 apeirogonal tiling : The square tiling honeycomb is a regular...

each. Sometimes the order-2 apeirogonal tiling is not included, as its two faces meet at more than one edge. For clarity, the tilings are not colored from...

In geometry, an apeirogonal hosohedron or infinite hosohedron is a tiling of the plane consisting of two vertices at infinity. It may be considered an...

square faces. Its dual tiling is an apeirogonal bipyramid. The apeirogonal tiling is the arithmetic limit of the family of prisms t{2, p} or p.4.4, as p tends...

operations. They are higher-dimensional analogues of the order-2 apeirogonal tiling and apeirogonal hosohedron. There are 15 flat regular honeycombs of hyperbolic...

with Infinite-order triangular tiling cells: {3,∞,p}. It is a part of a sequence of regular honeycombs with order-3 apeirogonal tiling vertex figures:...

is {∞,3,6}, with six order-3 apeirogonal tilings meeting at each edge. The vertex figure of this honeycomb is a triangular tiling, {3,6}. It has a quasiregular...

tiling. The apeirogonal antiprism can be constructed by applying an alternation operation to an apeirogonal prism. The dual tiling of an apeirogonal antiprism...

space. The order-6 hexagonal tiling honeycomb is analogous to the 2D hyperbolic infinite-order apeirogonal tiling, {∞,∞}, with infinite apeirogonal faces,...

sphere. The Schläfli symbol of the apeirogonal tiling honeycomb is {∞,8,3}, with three order-8 apeirogonal tilings meeting at each edge. The vertex figure...

In geometry, a binary tiling (sometimes called a Böröczky tiling) is a tiling of the hyperbolic plane, resembling a quadtree over the Poincaré half-plane...

be seen as similar to the order-3 apeirogonal tiling, {∞,3} of H2, with horocycles circumscribing vertices of apeirogonal faces. It has a total of five...

apeirogonal dihedron as a 2-dimensional tessellation: A regular ditope is an n-dimensional analogue of a dihedron, with Schläfli symbol {p,...,q,r,2}...

boundary) with infinitely many order-6 apeirogonal tilings existing around each vertex in an infinite-order square tiling vertex arrangement. It has a second...

infinite-order apeirogonal tiling, {∞,∞}, with infinite apeirogonal faces, and with all vertices on the ideal surface. The triangular tiling honeycomb...

honeycomb Hosohedron Dihedron Order-2 apeirogonal tiling Apeirogonal hosohedron Order-4 square hosohedral honeycomb Order-6 triangular hosohedral honeycomb...

honeycomb) with Schläfli symbol {∞,4,∞}. It has infinitely many order-4 apeirogonal tiling {∞,4} around each edge. All vertices are ultra-ideal (existing...

tiling, this restriction may be relaxed, since digons (2-gons) can be represented as spherical lunes, having non-zero area. Allowing m = 2 makes N 2 =...