In spherical geometry, an n-gonal hosohedron is a tessellation of lunes on a spherical surface, such that each lune shares the same two polar opposite...

polytopes, a notable example being the apeirogonal hosohedron, the limit of a general spherical hosohedron at infinity, composed of an infinite number of...

monogonal faces which share one 360° edge and one vertex. Its dual, a hosohedron, {2,1} has two antipodal vertices at the poles, one 360° lune face, and...

polyhedron: it exists as a spherical tiling of digon faces, called a pentagonal hosohedron with Schläfli symbol {2,5}. It has 2 (antipodal point) vertices, 5 edges...

most popular spherical polyhedron is the beach ball, thought of as a hosohedron. Some "improper" polyhedra, such as hosohedra and their duals, dihedra...

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...

spaced. The hosohedron {2,n} is dual to the dihedron {n,2}. Note that when n = 2, we obtain the polyhedron {2,2}, which is both a hosohedron and a dihedron...

vertices are equally spaced. The dual of an n-gonal dihedron is an n-gonal hosohedron, where n digon faces share two vertices. A dihedron can be considered...

sphere. A hosohedron is a tessellation of the sphere by lunes. A n-gonal regular hosohedron, {2,n} has n equal lunes of π/n radians. An n-hosohedron has dihedral...

stellated 120-cell Honeycomb Cubic honeycomb Hosohedron Dihedron Order-2 apeirogonal tiling Apeirogonal hosohedron Order-4 square hosohedral honeycomb Order-6...

prism can be constructed via the geometrical truncation of an n-gonal hosohedron, as well as through the cantellation or expansion of an n-gonal dihedron...

and two regular polygon caps. It can be seen as a truncated hexagonal hosohedron, represented by Schläfli symbol t{2,6}. Alternately it can be seen as...

number of unique forms to four: the apeirogonal tiling, the apeirogonal hosohedron, the apeirogonal prism, and the apeirogonal antiprism. Order-3 apeirogonal...

and two regular polygon caps. It can be seen as a truncated pentagonal hosohedron, represented by Schläfli symbol t{2,5}. Alternately it can be seen as...

cylinders is called a bicylinder. Topologically, it is equivalent to a square hosohedron. The intersection of three cylinders is called a tricylinder. A bisected...

filling half the plane; and secondly, its dual, {2,∞}, an apeirogonal hosohedron, seen as an infinite set of parallel lines. There are no regular plane...

rhombohedron, this has six pentagon faces and two triangle faces. Octagonal hosohedron: degenerate in Euclidean space, but can be realized spherically. The following...

images of both are given. The spherical tilings including the set of hosohedrons and dihedrons which are degenerate polyhedra. These symmetry groups are...

triacontahedron pentagonal hexecontahedron Dihedral regular dihedron hosohedron Dihedral uniform Dihedral others pyramids truncated trapezohedra gyroelongated...

and its eight vertices define a cube as their convex hull. The square hosohedron is another polyhedron with four faces, but it does not have triangular...

Subdivision of the Sphere, CRC Press, p. 463, ISBN 978-1-4665-0430-1, A hosohedron is only possible on a sphere. Kraynik, A.M.; Reinelt, D.A. (2007), "Foams...

Octahedron, Dodecahedron, Icosahedron Regular spherical polyhedron Dihedron, Hosohedron Kepler–Poinsot polyhedron (Regular star polyhedra) Small stellated dodecahedron...

= [4,2] = 16 D2h×Dih3 = Oh A13×6 [3[2,2]] = [4,3] = 48 C3v A2 [1,3] 6 hosohedron C4v BC2 [1,4] 8 C5v H2 [1,5] 10 C6v G2 [1,6] 12 Cnv I2(n) [1,n] 2n Cnv×Dih1...

number of unique forms to four: the apeirogonal tiling, the apeirogonal hosohedron, the apeirogonal prism, and the apeirogonal antiprism. Conway (2008),...

faithfully realized in Euclidean spaces. The digon is generalized by the hosohedron and higher dimensional hosotopes, which can all be realized as spherical...

symmetry [3,8] symmetry Starting solid Operation Symbol {p,q} Triangular hosohedron {2,3} Triangular dihedron {3,2} Tetrahedron {3,3} Cube {4,3} Octahedron...

number of unique forms to four: the apeirogonal tiling, the apeirogonal hosohedron, the apeirogonal prism, and the apeirogonal antiprism. Conway (2008),...

one vertex, and one edge, and can attached to a degenerate monogonal hosohedron hole, like a cylinder hole with zero radius. A face with a degenerate...

n } {\displaystyle {\begin{Bmatrix}2,n\end{Bmatrix}}} is a regular n-hosohedron, a degenerate polyhedron, but a valid tiling on the sphere with digon...

degenerate 4-dimensional case exists as 3-sphere tiling, a tetrahedral hosohedron. It is first in a dimensional series of uniform polytopes and honeycombs...