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math.MG2025
Volumes of Regular Hyperbolic Simplices
Zakhar Kabluchko, Philipp Schange
We derive an explicit formula for the volume of a regular simplex in the hyperbolic space of any dimension.
math.MG2025
Angles of orthocentric simplices
Zakhar Kabluchko, Philipp Schange
A -dimensional simplex in Euclidean space is called orthocentric if all of its altitudes intersect at a single point, referred to as the orthocenter. We explicitly compute the i…