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Petrie, J.F. (1938) Petrie Polygons. In: Coxeter, H.S.M., du Val, P., Flather, H.T., Petrie, J.F., Eds., The Fifty-Nine Icosahedra, University of Toronto Studies, Mathematical Series, 1-26.

has been cited by the following article:

• TITLE: Proving a Special Case of the Coxeter-Hadwiger Conjecture

  AUTHORS: István Lénárt

  KEYWORDS: Pythagorean Simplex, Coxeter Partition of a Pythagorean Simplex in n-Dimensional Space

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.8, August 25, 2025

  ABSTRACT: An orthoscheme or Pythagorean simplex is a solid in n-dimensional Euclidean space whose faces are right triangles. In 1956, Hadwiger asked whether an n-dimensional general (not necessarily Pythagorean) simplex can always be decomposed into a finite number of Pythagorean simplexes. Tschirpke proved in 1994 that this division is always possible in 5D space. Coxeter proved that a 3D Pythagorean simplex can be split into three smaller ones. In a 2024 paper, I generalized Coxeter’s trisection to prove that the dissection of an n-dimensional Pythagorean simplex into n pieces of the same type is possible if each leg of the original solid is equal to the unit distance. In the present paper, I extend this proof to an n-dimensional Pythagorean simplex with legs of arbitrary measure. This means the proof of the Hadwiger conjecture in the special case of a Pythagorean simplex.