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...

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...

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

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...

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

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...

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...

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...

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...

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...

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

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

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

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

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...

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

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...

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

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...

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

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...

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

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...

pentagonal embedding of the Petersen graph in the projective plane. The p-hosohedron is a regular map of type {2,p}. The Dyck map is a regular map of 12 octagons...

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...