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^^
Excellent. It is only necessary to know that
point x n-cube = n-cube
line segment x n-cube = (n+1)-cube
etc.
In fact, that n-cube x m-cube = (nm)-cube
...
Now the number of n-tetrahedra in a D-tetrahedron is given by C(D,n).
The generating function is (x+1)^D. But what does it mean
heuristically?