A dihedron is a type of polyhedron, made of two polygon faces which share the same set of n edges. In three-dimensional Euclidean space, it is degenerate if its faces are flat, while in three-dimensional spherical space, a dihedron with flat faces can be thought of as a lens, an example of which is the fundamental domain of a lens space L(p,q).[1] Dihedra have also been called bihedra,[2]flat polyhedra,[3] or doubly covered polygons.[3]
As a spherical tiling, a dihedron can exist as nondegenerate form, with two n-sided faces covering the sphere, each face being a hemisphere, and vertices on a great circle. It is regular if the vertices are equally spaced.
The dual of an n-gonal dihedron is an n-gonal hosohedron, where n digon faces share two vertices.
^Gausmann, Evelise; Roland Lehoucq; Jean-Pierre Luminet; Jean-Philippe Uzan; Jeffrey Weeks (2001). "Topological Lensing in Spherical Spaces". Classical and Quantum Gravity. 18 (23): 5155–5186. arXiv:gr-qc/0106033. Bibcode:2001CQGra..18.5155G. doi:10.1088/0264-9381/18/23/311. S2CID 34259877.
^Kántor, S. (2003), "On the volume of unbounded polyhedra in the hyperbolic space" (PDF), Beiträge zur Algebra und Geometrie, 44 (1): 145–154, MR 1990989, archived from the original (PDF) on 2017-02-15, retrieved 2017-02-14.
^ abO'Rourke, Joseph (2010), Flat zipper-unfolding pairs for Platonic solids, arXiv:1010.2450, Bibcode:2010arXiv1010.2450O
A dihedron is a type of polyhedron, made of two polygon faces which share the same set of n edges. In three-dimensional Euclidean space, it is degenerate...
can be constructed as a vertex on a great circle (equator). This forms a dihedron, {1,2}, with two hemispherical monogonal faces which share one 360° edge...
hexagonal beach ball, {2, 6}, is a hosohedron, and {6, 2} is its dual dihedron. During the 10th Century, the Islamic scholar Abū al-Wafā' Būzjānī (Abu'l...
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. All of these have...
regular solid with its face counted twice. Therefore, it is also called a dihedron (Greek: solid with two faces), which explains the name dihedral group (in...
hosohedron {2, n} is the n-gonal dihedron, {n, 2}. The polyhedron {2,2} is self-dual, and is both a hosohedron and a dihedron. A hosohedron may be modified...
are given. The spherical tilings including the set of hosohedrons and dihedrons which are degenerate polyhedra. These symmetry groups are formed from...
Euclidean plane, even when its dual order-2 apeirogonal tiling (infinite dihedron) is. A compound of two "line segment" digons, as the two possible alternations...
is the conformal map projection from the sphere to an unfolded square dihedron, developed by Charles Sanders Peirce in 1879. Each octant projects onto...
their vertices lie along a great circle. This is called a spherical square dihedron. The Schläfli symbol is {4,2}. Six squares can tile the sphere with 3 squares...
A grid on the square dihedron under inverse Peirce quincuncial projection is conformal except at four singularities around the equator, which become the...
the plane. There are two improper regular tilings: {∞,2}, an apeirogonal dihedron, made from two apeirogons, each filling half the plane; and secondly, its...
either an isotetrahedron or a rectangle dihedron and conversely, every net of an isotetrahedron or rectangle dihedron is a Conway tile. The Conway criterion...
coinciding edges, where the two edges attach to two coplanar faces, as a dihedron hole. (genus 1) with two (degenerate point or monogon) 1-holed-faces. V=10...
this construction from a degenerate "polyhedron" with only two faces (a dihedron). Chiral snub polyhedra do not always have reflection symmetry and hence...
Algorithm for Folding a Conway Tile into an Isotetrahedron or a Rectangle Dihedron", Journal of Information Processing, 28 (28): 750–758, doi:10.2197/ipsjjip...
height of the building. Danish Pavilion: designed by Tyge Hvass, this was a dihedron of reddish wood with a gabled roof, evoking a typical Danish mountain house...
considered as a degenerate regular prism. Therefore, it is also called a dihedron (Greek: solid with two faces), which explains the name dihedral group....
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