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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.
1991, J. H. Conway, N. J. A. Sloane, “The Cell Structures of Certain Lattices”, in Peter Hilton, Friedrich Hirzebruch, Reinhold Remmert, editors, Miscellanea Mathematica, page 90:
It is remarkable that the four-dimensional orthoplex is the same polytope as the four-dimensional hemicube.
2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things, page 412:
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.
^ Conway, J. H., Sloane, N. J. A. (1991) “The Cell Structures of Certain Lattices”, in Hilton, P., Hirzebruch, F., Remmert, R., editors, Miscellanea Mathematica, Berlin: Springer, →DOI, →ISBN, pages 89–90
