Advances in Applied Clifford Algebras

, Volume 23, Issue 4, pp 815–824 | Cite as

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

  • Carlos Castro PerelmanEmail author
  • Fang Fang
  • Klee Irwin


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].


Irreducible Representation Clifford Algebra Generalize Matrice High Derivative Gravity Regular Polytope 
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  1. 1.
    J. Kovacs, F. Fang, G. Sadler and K. Irwin, The Sum of Squares Law. arXiv: 1210.1446.Google Scholar
  2. 2.
    M. Hamermesh, Group Theory and its Applications to Physical Problems. Addison-Wesley, Reading (1962). Reprinted by Dover.Google Scholar
  3. 3.
    Miller W. Jr.: Symmetry Groups and their Applications. Academic Press, New York (1972)zbMATHGoogle Scholar
  4. 4.
    Cornwell J.F.: Group Theory in Physics. (Three volumes), Volume 1. Academic Press, New York (1997)Google Scholar
  5. 5.
    C. Castro and M. Pavsic, The Extended Relativity Theory in Clifford-spaces. Progress in Physics vol 1 (April 2005), 31.Google Scholar
  6. 6.
    Castro C., Pavsic M.: Higher Derivative Gravity and Torsion from the Geometry of C-spaces. Phys. Letts B 559, 74 (2003)ADSCrossRefzbMATHGoogle Scholar
  7. 7.
    Castro C., Pavsic M.: On Clifford algebras of spacetime and the Conformal Group. Int. J. Theor. Phys 42, 1693 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    R.Williams, The Geometrical Foundations of Natural Structure. Dover edition 1979.Google Scholar

Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Quantum Gravity Research GroupCaliforniaUSA

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