Definition:Simplicial Complex

Definition

Let $m \in \Z_{>0}$ be a (strictly) positive integer.

A simplicial complex is a finite set $K$ of simplices in $\R^m$ such that:

all faces of the simplices in $K$ are included

two simplices meet, if at all, in a common face.

Also see

• Results about simplicial complexes can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): combinatorial topology
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): simplicial complex
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): combinatorial topology
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): simplicial complex