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September 24, 2025

Quasi-arithmetic hyperbolic Coxeter prisms

Key Points

The study identifies precisely which hyperbolic Coxeter prisms are properly quasi-arithmetic or arithmetic.
Key findings include observations on commensurability classes and systoles related to the associated orbifolds.
This work builds on prior classification efforts from 1974, refining understanding of geometric properties.
Implications of these results extend to the classification and understanding of hyperbolic geometric structures.

Abstract

In 1974, Kaplinskaja classified all simplicial straight hyperbolic Coxeter prisms. In this paper, we determine precisely which of these prisms are properly quasi-arithmetic or arithmetic. We also present some observations regarding commensurability classes and systoles of the associated orbifolds.

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Quasi-arithmetic hyperbolic Coxeter prisms

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Abstract

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