This beach ball would be a hosohedron with 6 spherical lune faces, if the 2 white caps on the ends were removed and the lunes extended to meet at the poles.
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 vertices.
A regular n-gonal hosohedron has Schläfli symbol {2,n}, with each spherical lune having internal angle 2π/nradians (360/n degrees).[1][2]
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...
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...
polytopes, a notable example being the apeirogonal hosohedron, the limit of a general spherical hosohedron at infinity, composed of an infinite number of...
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...
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...
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...
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...
triangle shares an edge with another triangle (Johnson solid 26). Octagonal hosohedron: degenerate in Euclidean space, but can be realized spherically. Natural...
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...
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...
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...
number of unique forms to four: the apeirogonal tiling, the apeirogonal hosohedron, the apeirogonal prism, and the apeirogonal antiprism. Conway (2008),...
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...
faithfully realized in Euclidean spaces. The digon is generalized by the hosohedron and higher dimensional hosotopes, which can all be realized as spherical...
Global Information
