Law of Sums of the Squares of Areas, Volumes and Hyper-Volumes of Regular Polytopes from Clifford Algebras

Abstract

Inspired by the recent sums of the squares law obtained by [1] we derive the law of the sums of the squares of the areas, volumes and hyper-volumes associated with the faces, cells and hyper-cells of regular polytopes in diverse dimensions by using Clifford algebraic methods [5].

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Correspondence to Carlos Castro Perelman.

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Castro Perelman, C., Fang, F. & Irwin, K. Law of Sums of the Squares of Areas, Volumes and Hyper-Volumes of Regular Polytopes from Clifford Algebras. Adv. Appl. Clifford Algebras 23, 815–824 (2013). https://doi.org/10.1007/s00006-013-0403-7

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Keywords

  • Irreducible Representation
  • Clifford Algebra
  • Generalize Matrice
  • High Derivative Gravity
  • Regular Polytope