The most familiar spherical polyhedron is the football, thought of as a spherical truncated icosahedron.This beach ball would be a hosohedron with 6 spherical lune faces, if the 2 white caps on the ends were removed.
In geometry, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons. Much of the theory of symmetrical polyhedra is most conveniently derived in this way.
The most familiar spherical polyhedron is the soccer ball, thought of as a spherical truncated icosahedron. The next most popular spherical polyhedron is the beach ball, thought of as a hosohedron.
Some "improper" polyhedra, such as hosohedra and their duals, dihedra, exist as spherical polyhedra, but their flat-faced analogs are degenerate. The example hexagonal beach ball, {2, 6}, is a hosohedron, and {6, 2} is its dual dihedron.
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In geometry, a sphericalpolyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded...
Wenninger's Spherical models, polyhedra are given geodesic notation in the form {3,q+}b,c, where {3,q} is the Schläfli symbol for the regular polyhedron with...
In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) 'many', and ἕδρον (-hedron) 'base, seat') is a three-dimensional shape...
positive value of f, this exceeds 180°. Spherical astronomy Spherical conic Spherical distance SphericalpolyhedronSpherics Half-side formula Lénárt sphere Versor...
a (globally) projective polyhedron is a tessellation of the real projective plane. These are projective analogs of spherical polyhedra – tessellations...
football and team handball are perhaps the best-known example of a sphericalpolyhedron analog to the truncated icosahedron, found in everyday life. The...
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive...
projection based on a sphericalpolyhedron. Typically, the polyhedron is overlaid on the globe, and each face of the polyhedron is transformed to a polygon...
transforming polyhedra. A spherical lune is a digon whose two vertices are antipodal points on the sphere. A sphericalpolyhedron constructed from such digons...
triacontahedron has the most faces of any other strictly convex polyhedron where every face of the polyhedron has the same shape. Projected into a sphere, the edges...
Schläfli symbol {2,n}, with each spherical lune having internal angle 2π/nradians (360/n degrees). For a regular polyhedron whose Schläfli symbol is {m, n}...
linear-edged Schlegel diagram, or stereographic projection as a sphericalpolyhedron. These projections are also used in showing the four-dimensional...
such as the hemi-cube, which are the image of a 2 to 1 map of a sphericalpolyhedron with central symmetry. Their Wythoff symbols are of the form p/(p − q) p/q | r;...
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...
In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive (i.e., there is an isometry mapping any vertex onto any other)...
Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical...
In geometry, an octahedron (pl.: octahedra or octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron...
sphere. A geodesic polyhedron has straight edges and flat faces that approximate a sphere, but it can also be made as a sphericalpolyhedron (A tessellation...
The compound of five octahedra is one of the five regular polyhedron compounds, and can also be seen as a stellation. It was first described by Edmund...
octahedron. It has cubical or octahedral symmetry, and is the only convex polyhedron whose faces are all squares. Its generalization for higher-dimensional...
numbers of vertices (corners), edges and faces in the given polyhedron. Any convex polyhedron's surface has Euler characteristic χ = V − E + F = 2 ....
Replacing each face of the rhombic dodecahedron with a flat pyramid creates a polyhedron that looks almost like the disdyakis dodecahedron, and is topologically...
faces represent the 24 fundamental domains of tetrahedral symmetry. This polyhedron can be constructed from 6 great circles on a sphere. It can also be seen...
more specifically in polyhedral combinatorics, a Goldberg polyhedron is a convex polyhedron made from hexagons and pentagons. They were first described...
an indexed list of the uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger. The book was written as a guide book to building...
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