Hypercell (no ontology)
From Higher Dimensions Database
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.