List of noble polyhedra

Besides the tetragonal disphenoid, the rhombic disphenoid and the infinite family of crown polyhedra, there are 78 known non-exotic noble polyhedra, 9 of which are regular and 2 of which are fissary:

Tetrahedral symmetry
There exists only one noble polyhedron with tetrahedral/chiral tetrahedral symmetry: the tetrahedron.