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Regarding John Denker's homework problem.
Homework: As a function of D (the number of dimensions
in the hypercube), from D=1 to D=6, calculate the
number of d=0 corners, the number of d=1 edges,
the number of d=2 faces, the number of d=3 hyperfaces,
if you are interested in the numbers of lower dimensional
parts on the boundary of a D-dimensional simplex.
David Bowman
georgetowncollege.edu