
Journal for Geometry and Graphics 25 (2021), No. 2, 197204 Copyright Heldermann Verlag 2021 Dihedral Angles of 4Ball Tetrahedra Hidefumi Katsuura San Jose State University, San Jose, U.S.A. hidefumi.katsuura@sjsu.edu A tetrahedron is a 4ball tetrahedron if there are four externally tangent spheres centered at the vertices of the tetrahedron. It is known that a tetrahedron being a 4ball 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 4ball tetrahedron if, and only if three pairs of the sums of opposing dihedral angles are the same. Keywords: Fourball tetrahedron, balloon tetrahedron, edgeadditive tetrahedron, edgetangent sphere, circumscriptable tetrahedron, edgeincentric tetrahedron, dihedralangleadditive tetrahedron. MSC: 51M15; 51M04. [ Fulltextpdf (444 KB)] for subscribers only. 