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Bibliographic Details
Main Authors: Eldridge, Summer, Prabha, Adithya, Roger, Aiden, Roger, Cooper, Roldán, Érika, Toalá-Enríquez, Rosemberg
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2603.18638
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Table of Contents:
  • A polyform is a planar figure formed by gluing congruent regular polygons along entire edges. We study polyforms in hyperbolic ${p,q}$-tessellations and the extremal problem of minimizing the number of tiles needed to realize exactly $h$ holes. Denoting this minimum by $g_{p,q}(h)$, we establish general lower and upper bounds, compute exact values in several small cases, and give a sufficient structural condition for a polyform to have $h$ holes and $g_{p,q}(h)$ tiles.