Abstract.
Let Δ be an n-dimensional simplex in Euclidean space \({\mathbb{E}}^n\) contained in an n-dimensional closed ball B. The following question is considered. Given any point \(x \,{\in}\,\triangle\), does there exist a reflection \(r : {\mathbb{E}}^n \rightarrow {\mathbb{E}}^n\) in one of the facets of Δ such that \(r(x)\in B\)?
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Vince, A. A Simplex Contained in a Sphere. J. geom. 89, 169–178 (2008). https://doi.org/10.1007/s00022-008-1907-5
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DOI: https://doi.org/10.1007/s00022-008-1907-5