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2 votes
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Regarding fundamental domain of 2 genus surface

Let $\mathbb{H}^2$ be the hyperbolic plane with $(2,3,7)$ tiling. Let $\Gamma$ be a subgroup of $(2,3,7)$ triangle group such that $\mathbb{H}^2/\Gamma$ is the compact orientable surface of genus 2 ...
KAK's user avatar
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2 votes
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What groups of symmetry are most suited for filling uniformely a spherical 3D space, whilst possessing the lowest possible surface-to-volume ratio?

I am looking for the closest known approximate solution to Kelvin foams problem that would obey a spherical symmetry. One alternative way of formulating it: I am looking for an equivalent of Weaire–...
Andrei Kucharavy's user avatar
1 vote
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382 views

Which polygons tessellate the hyperbolic plane?

The packing fraction of a packing in some space is the fraction of the space filled by the figures making up the packing. It is well known that in Euclidean geometry, all triangles and all ...
Nandakumar R's user avatar
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