Dihedral Angles of 4-Ball Tetrahedra
Publication Date
1-1-2021
Document Type
Article
Publication Title
Journal for Geometry and Graphics
Volume
25
Issue
2
First Page
197
Last Page
204
Abstract
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
Department
Mathematics and Statistics
Recommended Citation
Hidefumi Katsuura. "Dihedral Angles of 4-Ball Tetrahedra" Journal for Geometry and Graphics (2021): 197-204.