# Platonic solids generate their four-dimensional analogues.

@article{Dechant2013PlatonicSG, title={Platonic solids generate their four-dimensional analogues.}, author={Pierre-Philippe Dechant}, journal={Acta crystallographica. Section A, Foundations of crystallography}, year={2013}, volume={69 Pt 6}, pages={ 592-602 } }

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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