Orthoplex

We made use of another way of considering the 120 cells, starting with the eight at the vertices of an orthoplex, that is, in the cells of a hypercube.

It is remarkable that the four-dimensional orthoplex is the same polytope as the four-dimensional hemicube.

The combinatorics of this case apply to all members of the Gosset series; in every case, their cells are simplexes and orthoplexes, the latter appearing with only half symmetry.