Proportional Tetrahedron

A commensurate tetrahedron is a tetrahedron whose equal heights are equal.

This definition can be replaced by any of the following:

• The projection of the tetrahedron onto a plane perpendicular to any bimedian is a rhombus.
• The edges of the described parallelepiped are equal.
• For each pair of opposite edges of the tetrahedron, the planes drawn through one of them and the middle of the second are perpendicular.
• A sphere can be inscribed in the described parallelepiped of a commensurate tetrahedron.