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

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

the order-3-6 apeirogonal honeycomb a regular space-filling tessellation (or honeycomb). Each infinite cell consists of an order-3 apeirogonal tiling whose...

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, 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...

boundary) with infinitely many order-5 apeirogonal tilings existing around each vertex in an infinite-order pentagonal tiling vertex arrangement. It has a second...

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...

heptagonal tiling honeycomb or 7,3,3 honeycomb a regular space-filling tessellation (or honeycomb). Each infinite cell consists of a heptagonal tiling whose...

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

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

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:...

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...

sphere. The Schläfli symbol of the apeirogonal tiling honeycomb is {∞,7,3}, with three order-7 apeirogonal tilings meeting at each edge. The vertex figure...

sphere. The Schläfli symbol of the apeirogonal tiling honeycomb is {∞,6,3}, with three order-6 apeirogonal tilings meeting at each edge. The vertex figure...

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

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

The order-5 hexagonal tiling honeycomb is similar to the 2D hyperbolic regular paracompact order-5 apeirogonal tiling, {∞,5}, with five apeirogonal faces...

2-dimensional hyperbolic geometry, the infinite-order hexagonal tiling is a regular tiling. It has Schläfli symbol of {6,∞}. All vertices are ideal, located at...

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

to the 2D hyperbolic pentaapeirogonal tiling, r{5,∞} with pentagon and apeirogonal faces. The truncated order-6 dodecahedral honeycomb, t0,1{5,3,6} has...

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

sphere. The Schläfli symbol of the apeirogonal tiling honeycomb is {∞,5,3}, with three order-5 apeirogonal tilings meeting at each edge. The vertex figure...

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

prism and apeirogonal antiprism. The stacking of the finite faces of these two prismatic tilings constructs one non-Wythoffian uniform tiling of the plane...

tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex. It is named as a triangular tiling elongated...

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

hosohedron is the n-gonal prism. In the limit, the hosohedron becomes an apeirogonal hosohedron as a 2-dimensional tessellation: Multidimensional analogues...

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

tiling, r{4,∞}, alternating apeirogonal and square faces: The truncated order-6 cubic honeycomb, t{4,3,6}, has truncated cube and triangular tiling facets...