What would you like to understand?

You interpret a complete graph as a simplex by keeping its vertices and edges, then filling in higher-dimensional cells such as 2-dimensional triangular faces, 3-dimensional solids, and 4-dimensional spaces. A complete graph on k vertices forms $a (k-1)$-simplex.

Conditions: The starting structure is a complete graph on k vertices.; Higher-dimensional cells are filled successively between existing lower-dimensional ones.

You interpret a complete graph as a simplex by keeping its vertices and edges, then filling in higher-dimensional cells such as 2-dimensional triangular faces, 3-dimensional solids, and 4-dimensional spaces. A complete graph on k vertices forms $a (k-1)$-simplex.

Conditions: The starting structure is a complete graph on k vertices.; Higher-dimensional cells are filled successively between existing lower-dimensional ones.