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...

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

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

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

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

truncated order-3 apeirogonal tiling, t{∞,3} with apeirogonal and triangle faces: The bitruncated hexagonal tiling honeycomb or bitruncated order-6 tetrahedral...

apeirogonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli symbol of the order-3-6...

The Schläfli symbol of the order-3-4 apeirogonal honeycomb is {∞,3,4}, with four order-3 apeirogonal tilings meeting at each edge. The vertex figure...

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...

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

apeirogonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli symbol of the order-3-5...

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...

are the infinite analogues of n-polytopes.: 22–25  Apeirogonal tiling Apeirogonal prism Apeirogonal antiprism Teragon, a fractal generalized polygon that...

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...

distance larger than zero, the faces are infinite polygons (a bit like the apeirogonal hosohedron's digon faces, having a width larger than zero, are infinite...

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...

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

In geometry, the infinite-order triangular tiling is a regular tiling of the hyperbolic plane with a Schläfli symbol of {3,∞}. All vertices are ideal,...

with alternate colored square faces. Its dual tiling is an apeirogonal bipyramid. The apeirogonal tiling is the arithmetic limit of the family of prisms...

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

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...

lattice in a Lie group. The vertices and edges of an order- k {\displaystyle k} apeirogonal tiling of the hyperbolic plane form a Bethe lattice of degree...

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

domain: . The order-4 square tiling honeycomb is analogous to the 2D hyperbolic infinite-order apeirogonal tiling, {∞,∞}, with infinite apeirogonal faces, and...

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...

infinite-order (ultraparallel) branches. The order-5 hexagonal tiling honeycomb is similar to the 2D hyperbolic regular paracompact order-5 apeirogonal tiling...

higher-dimensional analogues of the order-2 apeirogonal tiling and apeirogonal hosohedron. There are 15 flat regular honeycombs of hyperbolic 3-space: 4 are compact:...