**Simplices**:

0-dim (Point) $latex triangle_0 $

1-dim (Line) $latex triangle_1 $

2-dim (Triangle) $latex triangle_2 $

3-dim (Tetrahedron) $latex triangle_3 $

**Simplicial Complex**: built by various Simplices under some __rules__.

__Definitions of Simplex (S)__

Face

Orientation

Boundary ($latex delta $)

$latex displaystyle boxed {

delta(S) = sum_{i=0}^{n} (-1)^i (v_0 …hat v_i …v_n)}&fg=aa0000&s=3

$

**Theorem**: $latex boxed { delta ^2 (S) = 0}&fg=00bb00&s=4 $