64 lines from a quaternionic polytope
In the Coxeter Festschrift, the author presented two quaternionic 4-polytopes with 64 vertices [\textit{Ch. Davis, B. Gruenbaum} and \textit{F. A. Sherk}, `The geometric vein. The Coxeter Festschrift.' (1982; Zbl 0488.00015)]. In this note he shows that the angle of each pair of vertices of these polytopes, when regarded in complex 8-space, is a constant \(\alpha\) satisfying \(\cos^2\alpha= 1/9\).
scientific article; zbMATH DE number 1129447