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A polyhedron with extra triangular faces, given by the Schläfli symbol s{p; q}.

The south pole is the point on a sphere with minimum z-coordinate for a given coordinate system. For a rotating sphere like the Earth, the natural coordinate system is ...

Find the tunnel between two points A and B on a gravitating sphere which gives the shortest transit time under the force of gravity. Assume the sphere to be nonrotating, of ...

A spherical shell is a generalization of an annulus to three dimensions. A spherical shell is therefore the region between two concentric spheres of differing radii. The ...

The only irreducible spherical simplexes generated by reflection are A_n (n>=1), B_n (n>=4), C_n (n>=2), D_2^p (p>=5), E_6, E_7, E_8, F_4, G_3, and G_4. The only irreducible ...

A spheroidal section is the curve formed by the intersection of a plane with a spheroid. A spheroidal section is either a circle (for planes parallel to an equator, i.e., ...

The inversion of a spindle torus. If the inversion center lies on the torus, then the spindle cyclide degenerates to a parabolic spindle cyclide.

The square antiprism is the antiprism with square bases whose dual is the tetragonal trapezohedron. The square antiprism has 10 faces. The square antiprism with unit edge ...

The dual polyhedron of the cubitruncated cuboctahedron U_(16) and Wenninger dual W_(79).

A number of attractive 20-compounds of the regular tetrahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...