Two Quaternionic 4-Polytopes

S. G. Hoggar
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S. G. Hoggar: University of Glasgow, Department of Mathematics

A chapter in The Geometric Vein, 1981, pp 219-230 from Springer

Abstract: Abstract One property of a (convex) polytope in ℝ n is that the vertex set defines the actual subdivision into edges, triangles, etc. The cells (dimension n − 1) are the intersections of the convex hull of the vertices with its bounding hyperplanes. The cells intersect in (n − 2)-dimensional elements, and so on. All these are finite. But for a polytope in ℂ n convexity is not available; there is some latitude as to the various elements (now subspaces), subject to suitable conditions on their incidences. For example the fractional polytope $$ \frac{1}{3}\gamma _3^3 $$ and generalized cross polytope $$ \beta _3^3 $$ [10] agree as to vertices and “edges,” but the first has 18 “triangles” whereas the second has 27.

Keywords: Symmetry Group; Reflection Group; Dimensional Element; Coxeter Diagram; Unitary Reflection (search for similar items in EconPapers)
Date: 1981
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DOI: 10.1007/978-1-4612-5648-9_14

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