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Midsphere Tetrahedra and the Canonical Tetrahedron

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A midsphere polyhedron is one in which all edges are tangent to a unit sphere. A canonical polyhedron is a midsphere polyhedron such that the centroid of the tangent points is at the center of the unit sphere.

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There are many midsphere tetrahedra, but the canonical tetrahedron (a regular tetrahedron) is unique.

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Contributed by: Ed Pegg Jr (August 2022)
Open content licensed under CC BY-NC-SA

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