# Volumes of Regular Hyperbolic Simplices

**Authors:** Zakhar Kabluchko, Philipp Schange

arXiv: 2508.20450 · 2025-11-18

## TL;DR

This paper provides an explicit formula for calculating the volume of regular simplices in hyperbolic space across any dimension, facilitating precise geometric analysis.

## Contribution

It introduces a novel explicit formula for the volume of regular hyperbolic simplices in arbitrary dimensions, advancing geometric computation methods.

## Key findings

- Derived a general volume formula for hyperbolic simplices
- Enabled precise volume calculations in higher dimensions
- Facilitated geometric analysis in hyperbolic spaces

## Abstract

We derive an explicit formula for the volume of a regular simplex in the hyperbolic space of any dimension.

## Full text

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## Figures

3 figures with captions in the complete paper: https://tomesphere.com/paper/2508.20450/full.md

## References

33 references — full list in the complete paper: https://tomesphere.com/paper/2508.20450/full.md

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Source: https://tomesphere.com/paper/2508.20450