64 lines from a quaternionic polytope. (English) Zbl 0897.52001
In the Coxeter Festschrift, the author presented two quaternionic 4-polytopes with 64 vertices [Ch. Davis, B. Gruenbaum and 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 \(\cos^2\alpha= 1/9\).
Reviewer: R.Bödi (Tübingen)
MSC:
| 52B11 | \(n\)-dimensional polytopes |
| 51F15 | Reflection groups, reflection geometries |
| 68R99 | Discrete mathematics in relation to computer science |
| 51M20 | Polyhedra and polytopes; regular figures, division of spaces |
| 05B30 | Other designs, configurations |
