A cell complex or simply complex in
is a set
of convex polyhedra (called
cells) in
satisfying two conditions:
(1) Every face of a cell is a cell (i.e. in
), and (2) If
and
are
cells, then their intersection is a common face of both.
A simplicial complex is a cell complex whose cells are all
simplices.
The body of a complex
is the union of all cells.
When a subset
of
is the body of a simplicial complex
,
then
is said to be a triangulation of
.
For a finite set
of points in
, a triangulation of
is a simplicial complex
with
.