Four-Dimensional Space-Filling Polyhedra: Definition & Examples

A surface-filling polyhedron (also called a space-filling polyhedron, a polyhedron-filling space, a polyhedron, or a stereohedron) is a three-dimensional polyhedron that completely fills the space. This means that there are no gaps between any two polyhedra, and the polyhedra do not overlap. For example, a cube is a surface-filling polyhedron, as it completely fills its bounding box.

A four surface filling is a 4-dimensional polyhedron that completely fills a space. This means that there are no gaps between any two polyhedra, and the polyhedra do not overlap. For example, a tesseract (also known as an 8-cell or an octachoron) is a four-dimensional surface-filling polyhedron.