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A generalization of a solid such as a cube or a sphere to more than three dimensions. A four-dimensional version of a polyhedron is known as a polytope.

The principal normal indicatrix of a closed space curve with nonvanishing curvature bisects the area of the unit sphere if it is embedded.

A small circle is a spheric section that does not contain a diameter of the sphere (Kern and Bland 1948, p. 87; Tietze 1965, p. 25).

A polyhedron consisting of a n-gon, a parallel 2n-gon rotated a half-edge turn, and a band of paired triangles separated by pentagons. The only true member giving a ...

Enclose a sphere in a cylinder and cut out a spherical segment by slicing twice perpendicularly to the cylinder's axis. Then the lateral surface area of the spherical segment ...

In its original form, the Poincaré conjecture states that every simply connected closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense) S^3, ...

The surface of revolution obtained by cutting a conical "wedge" with vertex at the center of a sphere out of the sphere. It is therefore a cone plus a spherical cap, and is a ...

A spherical sector is a solid of revolution enclosed by two radii from the center of a sphere. The spherical sector may either be "open" and have a conical hole (left figure; ...

Cohomotopy groups are similar to homotopy groups. A cohomotopy group is a group related to the homotopy classes of maps from a space X into a sphere S^n.

A compact surface is a surface which is also a compact set. A compact surface has a triangulation with a finite number of triangles. The sphere and torus are compact.