MathDB
Existence of convex polyhedron with vertices on sphere

Source:

January 3, 2011
geometry3D geometrysphereratiogeometry unsolved

Problem Statement

Show that there exists a convex polyhedron with all its vertices on the surface of a sphere and with all its faces congruent isosceles triangles whose ratio of sides are 3:3:2\sqrt{3} :\sqrt{3} :2.