Building off of What are the formulas for the number of vertices, edges, faces, cells, 4-faces, ..., $n$-faces, of convex regular polytopes in $n \geq 5$ dimensions? ,
Are there formulas for the number of 6-faces, 5-faces, 4-faces, etc for an arbitrary 7-polytope? For example, the Hexipentiruncitruncated_7-simplex wikipedia page below is blank except for the edges and the vertices. Do methods exist to calculate the number of 6 faces, 5 faces, 4 faces?
https://en.wikipedia.org/wiki/Hexicated_7-simplexes#Hexipentiruncitruncated_7-simplex