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arXiv · 2603.18638

Holey Hyperbolic Polyforms

Summer Eldridge·Adithya Prabha·Aiden Roger·Cooper Roger·Érika Roldán·Rosemberg Toalá-Enríquez
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Abstract

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.

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Summer Eldridge, Adithya Prabha, Aiden Roger, Cooper Roger, Érika Roldán, Rosemberg Toalá-Enríquez. 2026-03-19. Holey Hyperbolic Polyforms. https://arxiv.org/abs/2603.18638

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