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Genus 1. A periodic tiling divided by its own lattice is a graph on a torus, and the battery is replaced by a homology class.

Hyperbolic. Infinite, so there is nothing to divide by: square a ball with its boundary shorted, and the answer is a cylinder.

Icosahedron halved · shico-half-6-00001

22 vertices · 60 edges · 40 faces · 16 distinct rectangles · symmetry order 4

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Genus 1. A periodic tiling divided by its own lattice is a graph on a torus, and the battery is replaced by a homology class.

Hyperbolic. Infinite, so there is nothing to divide by: square a ball with its boundary shorted, and the answer is a cylinder.

22 vertices · 60 edges · 40 faces · 16 distinct rectangles · symmetry order 4

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