Generalization of Schlafli formula to the volume of a spherically faced simplex
classification
🧮 math.DG
math.AGmath.CVmath.MG
keywords
identitiesfacedformulasimplexsphericallyvolumearrangementscayley-menger
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We present two identities (contiguity relation and variation formula) concerning the volume of a spherically faced simplex in the Euclidean space. These identities are described in terms of Cayley-Menger determinants and their differentials involved with hypersphere arrangements. They are derived as a limit of fundamental identities for hypergeometric integrals.
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