Isocanted cube: the lower Lebesgue volumes, incidence numbers and symmetries of this d–dimensional tile
DOI:
https://doi.org/10.17398/Keywords:
tile space, symmetry group, face volume, cubical zonotope, isocanted cube, incidence number, perturbationAbstract
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).
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