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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 ...
Four numbering schemes for the uniform polyhedra are in common use, distinguished by letters: [C] Coxeter et al., 1954, showed the convex forms as figures 15 through 32; three prismatic forms, figures 33–35; and the nonconvex forms, figures 36–92.
If you expand an icosidodecahedron by moving the faces away from the origin the right amount, without changing the orientation or size of the faces, and patch the square holes in the result, you get a rhombicosidodecahedron.
The March 1, 1943, edition of Life magazine included a photographic essay titled "Life Presents R. Buckminster Fuller's Dymaxion World", illustrating a projection onto a cuboctahedron, including several examples of possible arrangements of the square and triangular pieces, and a pull-out section of one-sided magazine pages with the map faces printed on them, intended to be cut out and glued to ...
In 4-dimensions a 3-sphere is a generalized sphere. It can contain regular digon lunes as {2} θ,φ , where θ and φ are two dihedral angles. For example, a regular hosotope {2,p,q} has digon faces, {2} 2π/p,2π/q , where its vertex figure is a spherical platonic solid , {p,q}.
Finite spherical symmetry groups are also called point groups in three dimensions.There are five fundamental symmetry classes which have triangular fundamental domains: dihedral, cyclic, tetrahedral, octahedral, and icosahedral symmetry.
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A midsphere of a three-dimensional convex polyhedron is defined to be a sphere that is tangent to every edge of the polyhedron. That is to say, each edge must touch it, at an interior point of the edge, without crossing it. Equivalently, it is a sphere that contains the inscribed circle of every face of the polyhedron. [2]
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