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arXiv · 1103.2051

Regular tessellations of the hyperbolic plane by fundamental domains of a Fuchsian group

Robert Yuncken
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Abstract

For positive integers p and q with 1/p + 1/q < 1/2, a tessellation of type {p,q} is a tessellation of the hyperbolic plane by regular p-gons with q p-gons meeting at each vertex. In this paper, a necessary and sufficient condition on the integers p and q is established to determine when a tessellation of type {p,q} can be realized as a tessellation of the hyperbolic plane by fundamental domains of some Fuchsian group. Specifically, a tessellation of type {p,q} is a tessellation by fundamental domains if and only if q has a prime divisor less than or equal to p.

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Robert Yuncken. 2011-03-10. Regular tessellations of the hyperbolic plane by fundamental domains of a Fuchsian group. https://arxiv.org/abs/1103.2051

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