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The construction of polyhedra using identical building blocks. The illustrations above show such constructions for the cuboctahedron, octahedron rhombic dodecahedron, and ...

A holyhedron is polyhedron whose faces and holes are all finite-sided polygons and that contains at least one hole whose boundary shares no point with a face boundary. D. ...

A hyperbolic version of the Euclidean dodecahedron. Hyperbolic three-space can be tessellated with hyperbolic dodecahedra whose intermediate dihedral angles are 60, 72, or 90 ...

A polyhedron in a hyperbolic geometry.

A hyperbolic version of the Euclidean tetrahedron.

The icosidodecadodecahedron is the uniform polyhedron with Maeder index 44 (Maeder 1997), Wenninger index 83 (Wenninger 1989), Coxeter index 56 (Coxeter et al. 1954), and ...

The icositruncated dodecadodecahedron, also called the icosidodecatruncated icosidodecahedron, is the uniform polyhedron with Maeder index 45 (Maeder 1997), Wenninger index ...

The sphere with respect to which inverse points are computed (i.e., with respect to which geometrical inversion is performed). For example, the cyclides are inversions in a ...

The inverted snub dodecadodecahedron is the uniform polyhedron with Maeder index 60 (Maeder 1997), Wenninger index 114 (Wenninger 1989), Coxeter index 76 (Coxeter et al. ...

For every positive integer n, there exists a sphere which has exactly n lattice points on its surface. The sphere is given by the equation ...