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A perfect cuboid is a cuboid having integer side lengths, integer face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2), (3) and an ...

A polyhedron compound is an arrangement of a number of interpenetrating polyhedra, either all the same or of several distinct types, usually having visually attractive ...

A spherical ring is a sphere with a cylindrical hole cut so that the centers of the cylinder and sphere coincide, also called a napkin ring. Let the sphere have radius R and ...

A number of attractive tetrahedron 10-compounds can be constructed. The first (left figures) can be obtained by combining tetrahedron 5-compounds of opposite chirality ...

The truncated great dodecahedron is the uniform polyhedron with Maeder index 37 (Maeder 1997), Wenninger index 75 (Wenninger 1989), Coxeter index 47 (Coxeter et al. 1954), ...

There are least two Bang's theorems, one concerning tetrahedra (Bang 1897), and the other with widths of convex domains (Bang 1951). The theorem of Bang (1897) states that ...

The three points determined on three coplanar edges of a tetrahedron by the external bisecting planes of the opposite dihedral angles are collinear. Furthermore, this line ...

The dodecahedron-icosahedron compound is a polyhedron compound consisting of a dodecahedron and its dual the icosahedron. In the compound, the dodecahedron and icosahedron ...

A number of attractive 2-compounds of the regular dodecahedron can be constructed. The first (left figures) has the symmetry of the cube and arises by combining two regular ...

A ruled surface is called a generalized cylinder if it can be parameterized by x(u,v)=vp+y(u), where p is a fixed point. A generalized cylinder is a regular surface wherever ...