Isocanted cube: the lower Lebesgue volumes, incidence numbers and symmetries of this d–dimensional tile

• M. J. de la Puente ^[1]
  1. [1] Departamento de Álgebra, Geometrı́a y Topologı́a, Facultad de Matemáticas Universidad Complutense, 28040 Madrid, Spain
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 40, Nº 1, 2025, págs. 1-26
• Idioma: inglés
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• Resumen

  • Let d ≥ 2. In this paper we prove that Id(ℓ, a) fills Rd face–to–face by translations. We prove that the symmetry group of Id(ℓ, a) contains the product of cyclic groups Cd × C2 as a subgroup. We compute the Lebesgue j–volume (i.e., the sum of the Lebesgue j–measures of the j–faces) of Id(ℓ, a), for 1 ≤ j < d. We compute the incidence numbers (as defined by Grünbaum) of the faces of Id(ℓ, a).