Spherical tetrahedra with rational volume, and spherical Pythagorean triples

DOI10.1090/mcom/3496zbMath1440.51001arXiv1811.06598OpenAlexW2995589062WikidataQ114094324 ScholiaQ114094324MaRDI QIDQ4960085

Alexander Kolpakov, Sinai Robins

Publication date: 8 April 2020

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.06598

zbMATH Keywords

spherical geometrytrigonometric Diophantine equationsrational spherical tetrahedra

Mathematics Subject Classification ID

Polyhedra and polytopes; regular figures, division of spaces (51M20) Lattices and convex bodies (number-theoretic aspects) (11H06) Length, area and volume in real or complex geometry (51M25) Reflection groups, reflection geometries (51F15)

Uses Software

• SageMath
• SymPy

Cites Work

• Unnamed Item
• On a problem of Fenchel
• The volume of the Lambert cube in spherical space
• Lambert cubes generating discrete reflection groups
• A characterization of Gram matrices of polytopes
• Discrete groups generated by reflections
• Volume formula for a \(\mathbb Z_2\)-symmetric spherical tetrahedron through its edge lengths
• Foundations of Hyperbolic Manifolds
• Trigonometric diophantine equations (On vanishing sums of roots of unity)
• Spherical simplices generating discrete reflection groups

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