It is unknown if the Cube was actually built through the cubic honeycombs using the Schläfli symbol.
A Schläfli symbol is closely related to reflection symmetry groups, also called Coxeter groups, given with the same indices, but square brackets instead p,q,r,....
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The orthoplex faces are constructed from the Coxeter group Dn−1 and have a Schlafli symbol of {31,n−1,1} rather than the regular {3n−2,4}.