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A figure used in many Asian cultures to symbolize the unity of the two "opposite" female and male elements, the "yin" and "yang." The solid and hollow parts composing the ...

The volumes of any n n-dimensional solids can always be simultaneously bisected by a (n-1)-dimensional hyperplane. Proving the theorem for n=2 (where it is known as the ...

The regular octahedron, often simply called "the" octahedron, is the Platonic solid with six polyhedron vertices, 12 polyhedron edges, and eight equivalent equilateral ...

Two mathematical objects are said to be homotopic if one can be continuously deformed into the other. For example, the real line is homotopic to a single point, as is any ...

The quasirhombicosidodecahedron is the uniform polyhedron with Maeder index 67 (Maeder 1997), Wenninger index 105 (Wenninger 1989), Coxeter index 84 (Coxeter et al. 1954), ...

The quasirhombicuboctahedron is the name given by Wenninger (1989, p. 132) to the uniform polyhedron with Maeder index 17 (Maeder 1997), Wenninger index 85 (Wenninger 1989), ...

A conical wedge is an ungula obtained by cutting a solid cone with a plane placed at an angle oblique to its base. For the special conical wedge obtained from a cone of ...

A cork plug is a three-dimensional solid that can stopper a square, triangular, or circular hole. There is an infinite family of such shapes. The shape with smallest volume ...

Goldberg polyhedra are convex polyhedra first described by Goldberg (1937) and classified in more detail by Hart (2013) for which each face is a regular pentagon or regular ...

The solid cut from a horizontal cylinder of length L and radius R by a single plane oriented parallel to the cylinder's axis of symmetry (i.e., a portion of a horizontal ...