# Hypercell (InstanceTopic, 2)

### From Higher Dimensions Database

(Redirected from Hypersurface)

A **hypercell** is a part of the surface of a shape. Hypercells of any given dimension are separated from each other by hypercells of one dimension less.

Specific terms for hypercells in dimensions 0-3 are *vertex*, *edge*, *face*, *cell*. Hypercells one dimension lower than that of the shape in question are called *facets*, for example, the facets of a cube are faces (since the cube is 3-dimensional and faces are 2-dimensional), the facets of a pentachoron are cells, and the facets of a decagon are edges.

The collective term for all facets of a shape is the *boundary* or *hypersurface* of that shape. Specific terms are *perimeter*, *surface* and *rind* for the boundaries of 2-4 dimensional shapes respectively.