Hi,

 

I was wondering what applications exist for n-dimensional figures (eg tesseract, hypercube). Could we start with 4-space?

The notion of a simplex is important in algebraic topology. Simplices are used to construct an interesting class of topological spaces known as simplicial complexes. These spaces are built from simplices "glued together". The simplicial complexes are fundamental in defining simplicial homology.

 

I hope that helps, even if it does not really answer your question