1978 USAMO #4
Source:
August 16, 2011
AMCUSA(J)MOUSAMOgeometry3D geometrytetrahedronsphere
Problem Statement
(a) Prove that if the six dihedral (i.e. angles between pairs of faces) of a given tetrahedron are congruent, then the tetrahedron is regular.(b) Is a tetrahedron necessarily regular if five dihedral angles are congruent?