Simplicial Complex

Math Online Tom Circle

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
$

image

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

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About tomcircle

Math amateur
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