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...

a (globally) projective polyhedron is a tessellation of the real projective plane. These are projective analogs of spherical polyhedra – tessellations...

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 figure...

projection based on a spherical polyhedron. Typically, the polyhedron is overlaid on the globe, and each face of the polyhedron is transformed to a polygon...

packing Spherical coordinates Spherical cow Spherical helix, tangent indicatrix of a curve of constant precession Spherical polyhedron Sphericity Tennis...

The spherical cube represents the spherical polyhedron, which can be modeled by the arc of great circles, creating bounds as the edges of a spherical square...

topologically self-dual. Projective polyhedron Skew apeirohedron (infinite skew polyhedron) Spherical polyhedron Toroidal graph Whiteley (1979); Stewart...

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...

55.288a^{3}.\end{aligned}}} The sphericity of a polyhedron Ψ {\displaystyle \Psi } describes how closely a polyhedron resembles a sphere. It can be defined...

spherical distance Lenart sphere Schwarz triangle Spherical geometry Spherical polyhedron Triangulation (surveying) Todhunter, I. (1886). Spherical Trigonometry...

transforming polyhedra. A spherical lune is a digon whose two vertices are antipodal points on the sphere. A spherical polyhedron constructed from such digons...

In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive—there is an isometry mapping any vertex onto any other. It follows...

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...

positive value of f, this exceeds 180°. Spherical astronomy Spherical conic Spherical distance Spherical polyhedron Spherics Half-side formula Lénárt sphere Versor...

Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical...

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...

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...

or intersphere of a convex polyhedron is a sphere which is tangent to every edge of the polyhedron. Not every polyhedron has a midsphere, but the uniform...

numbers of vertices (corners), edges and faces in the given polyhedron. Any convex polyhedron's surface has Euler characteristic   χ = V − E + F = 2   ....

value for density corresponds to the number of times the associated spherical polyhedron covers the sphere. ∑ i d v i v i − e + ∑ i d f i f i = 2 D {\displaystyle...

given manifold. If K and L are spherical (that is, tessellations of a topological sphere), then P is called locally spherical and corresponds itself to a...

such as the hemi-cube, which are the image of a 2 to 1 map of a spherical polyhedron with central symmetry. Their Wythoff symbols are of the form p/(p − q) p/q | r;...

tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices...

form a convex polyhedron called its convex hull. A compound is a faceting of its convex hull.[citation needed] Another convex polyhedron is formed by the...

A dihedron (pl. dihedra) is a type of polyhedron, made of two polygon faces which share the same set of n edges. In three-dimensional Euclidean space,...

dodecahedron. The edges of a spherical disdyakis dodecahedron belong to 9 great circles. Three of them form a spherical octahedron (gray in the images...

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...

infinite family of trapezohedra, face-transitive polyhedra. Its dual polyhedron is the pentagonal antiprism. As a decahedron it has ten faces which are...

Three-dimensional space Regular polyhedron Platonic solid: Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron Regular spherical polyhedron Dihedron, Hosohedron...