Tileable Surfaces

Published 15 Jul 2025 in math.DG, cs.CG, and math.CO | (2507.11281v1)

Abstract: We define a class of $C^k$-regular surfaces, $k \geq 1$, \emph{tileable surfaces}, that admit geometric tilings by a finite number of congruence classes of tiles. We show how to construct many examples, and examine the relationship with the well known tilings of the plane and sphere, as well as monohedral polyhedral surfaces.

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