... Pairs 41720.3 Properties of + and × 41920.4 Arithmetic of Triples and Quadruples 42120.5 Quaternions, Geometry, and Physics 42420.6 Octonions 42820.7 Why C, H,andO Are Special 43020.8 Biographical ... 45421.7 Rings and Fields 45721.8 Biographical Notes: Dedekind, Hilbert, and Noether 45922 Topology 46722.1 Geometry and Topology 46822.2 Polyhedron Formulas of Descartes and Euler 46922.3 ... octahedron, and it is also the same for the do-decahedron and the icosahedron. This implies that the cube and octahedron canbe exchanged in Kepler’s construction, as can the dodecahedron and the...