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Milnor (1956) found more than one smooth structure on the seven-dimensional hypersphere. Generalizations have subsequently been found in other dimensions. Using surgery ...

The circumsphere of given set of points, commonly the vertices of a solid, is a sphere that passes through all the points. A circumsphere does not always exist, but when it ...

The insphere of a solid is a sphere that is tangent to all faces of the solid. An insphere does not always exist, but when it does, its radius r is called the inradius and ...

Is it possible to cover completely the surface of a sphere with congruent, nonoverlapping arcs of great circles? Conway and Croft (1964) proved that it can be covered with ...

A torispherical dome is the surface obtained from the intersection of a spherical cap with a tangent torus, as illustrated above. The radius of the sphere R is called the ...

The Reuleaux tetrahedron, sometimes also called the spherical tetrahedron, is the three-dimensional solid common to four spheres of equal radius placed so that the center of ...

The n-ball, denoted B^n, is the interior of a sphere S^(n-1), and sometimes also called the n-disk. (Although physicists often use the term "sphere" to mean the solid ball, ...

Half of a sphere cut by a plane passing through its center. A hemisphere of radius r can be given by the usual spherical coordinates x = rcosthetasinphi (1) y = ...

How can n points be distributed on a unit sphere such that they maximize the minimum distance between any pair of points? This maximum distance is called the covering radius, ...

The Voronov-Neopryatnaya-Dergachev graphs are two graphs on 372 and 972 vertices which have unit-distance embeddings with all vertices on a sphere and chromatic number 5. The ...