Platonic solids generate their four-dimensional analogues.

  title={Platonic solids generate their four-dimensional analogues.},
  author={Pierre-Philippe Dechant},
  journal={Acta crystallographica. Section A, Foundations of crystallography},
  volume={69 Pt 6},
  • Pierre-Philippe Dechant
  • Published 2013
  • Mathematics, Physics, Medicine
  • Acta crystallographica. Section A, Foundations of crystallography
This paper shows how regular convex 4-polytopes - the analogues of the Platonic solids in four dimensions - can be constructed from three-dimensional considerations concerning the Platonic solids alone. Via the Cartan-Dieudonné theorem, the reflective symmetries of the Platonic solids generate rotations. In a Clifford algebra framework, the space of spinors generating such three-dimensional rotations has a natural four-dimensional Euclidean structure. The spinors arising from the Platonic… Expand

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