Abstract
It is shown that the growth rate [Formula: see text] of any [Formula: see text] faces Dirichlet tiling of [Formula: see text] is at most [Formula: see text], for an [Formula: see text], depending only on [Formula: see text] and [Formula: see text]. We do not know if there is a universal [Formula: see text], such that [Formula: see text] upperbounds the growth rate for any [Formula: see text]-regular tiling, when [Formula: see text]?
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