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arXiv · 1811.06598

Spherical tetrahedra with rational volume, and spherical Pythagorean triples

Alexander Kolpakov·Sinai Robins
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Abstract

We study spherical tetrahedra with rational dihedral angles and rational volumes. Such tetrahedra occur in the Rational Simplex Conjecture by Cheeger and Simons, and we supply vast families, discovered by computational efforts, of positive examples that confirm this conjecture. As a by-product, we also obtain a classification of all spherical Pythagorean triples, previously found by Smith.

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Alexander Kolpakov, Sinai Robins. 2018-11-15. Spherical tetrahedra with rational volume, and spherical Pythagorean triples. https://arxiv.org/abs/1811.06598

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