nLab
T-complex

A $T$-complex is a higher-dimensional combinatorial structure with a class of designated thin elements. The concept can be made sense of for various shapes:

• simplicial T-complex;
• cubical T-complex.

In general, the requirements are:

1. Every degenerate element is thin.
2. Every hollow shape has a unique thin filler.
3. If a thin element has every face but one also thin, then the last face is thin as well.