Adinkras From Ordered Quartets of BC${}_4$ Coxeter Group Elements and Regarding 1,358,954,496 Matrix Elements of the Gadget

Abstract

We examine values of the Adinkra Holoraumy-induced Gadget representation space metric over all possible four-color, four-open node, and four-closed node adinkras. Of the 1,358,954,496 gadget matrix elements, only 226,492,416 are non-vanishing and take on one of three values: $-1/3$, $1/3$, or $1$ and thus a subspace isomorphic to a description of a body-centered tetrahedral molecule emerges.Comment: LaTeX twice, 56pp, 30 tables, 5 figures, latest version includes link to updated code, minor corrections, and additional support about inequivalent representations and tetrahedral geometry comments added along with observations about similarity with results previously found by Nekraso