Spherical polyhedron - Wikipedia
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. A polyhedron whose vertices are equidistant from its center can be conveniently studied by projecting its edges onto the sphere to obtain a corresponding ...
spherical polyhedra
Our earth looks like this polyhedron, but it is much nicer! These polyhedra are constructed starting from Plato's polyhedra; a tessellation is drawn on each face and the central projection on the circumsphere defines the new vertices. Fuller widely popularized the …
Spherical Polyhedron -- from Wolfram MathWorld
2024年12月18日 · A spherical polyhedron is set of arcs on the surface of a sphere corresponding to the projections of the edges of a polyhedron. The images above illustrate the spherical polyhedron for the Platonic solids with the arcs extended radially inward for easier visualization.
Spherical polyhedron - Polytope Wiki
A spherical polyhedron is a type of non-Euclidean polyhedron that is a tiling of the sphere where all edges are great arcs. Usually it is implied that the faces are convex. Self-intersection may or may not be allowed. The regular spherical polyhedra are spherical projections of the Platonic solids, the regular hosohedra, and the regular dihedra ...
As. 6B Spherical Polyhedra - University of Washington
Spherical Form of Polyhedron = spherical tessellation. We have studied the regular polyhedra (Platonic solids) and some of the semiregular (Archimedean) polyhedra in 444. Each of these polyhedra can be inscribed in a sphere. This means that the vertices of one of these polyhedra are points on a sphere.
The Geometry of the Sphere 6 - math.csi.cuny.edu
The spherical polyhedron has V vertices, E edges and F faces, just like P does. Furthermore, since the center of the sphere was chosen inside P , the spherical polyhedron covers the entire sphere. Hence the spherical polyhedron is a division of the sphere into F disjoint spherical polygons, which we will call Q 1 , ... , Q F .
Spherical polyhedron - Wikiwand
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. A polyhedron whose vertices are equidistant from its center can be conveniently studied by projecting its edges onto the sphere to obtain a corresponding ...
Category : Spherical polyhedra - Wikimedia
In mathematics, a spherical polyhedron is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons.
Spherical polyhedron - Semantic Scholar
In mathematics, 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.
Plato suggested that the geometric forms of the smallest particles of these elements are regular polyhedra. Fire is represented by the tetrahedron, earth the cube, air the octahedron, water the icosahedron, and the almost-spherical dodecahedron, the universe.