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Journal for Geometry and Graphics 25 (2021), No. 2, 197--204
Copyright Heldermann Verlag 2021

Dihedral Angles of 4-Ball Tetrahedra

Hidefumi Katsuura
San Jose State University, San Jose, U.S.A.

A tetrahedron is a 4-ball tetrahedron if there are four externally tangent spheres centered at the vertices of the tetrahedron. It is known that a tetrahedron being a 4-ball tetrahedron is equivalent to (1) three pairs of the sum of opposing edge lengths are the same, and to (2) there is a sphere tangent to each edge of the tetrahedron. We will prove that a tetrahedron is a 4-ball tetrahedron if, and only if three pairs of the sums of opposing dihedral angles are the same.

Keywords: Four-ball tetrahedron, balloon tetrahedron, edge-additive tetrahedron, edge-tangent sphere, circumscriptable tetrahedron, edge-incentric tetrahedron, dihedral-angle-additive tetrahedron.

MSC: 51M15; 51M04.

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