List of noble polyhedra

1 dual pair with 24 vertices, 72 edges, and 24 pentagonal faces,

2 chiral self-duals with 24 vertices, 72 edges, and 24 pentagonal faces,

2 stellations of the icosahedron with 60 vertices, 90 edges, and 20 enneagrammic faces, and their duals, which are:

2 facetings of the dodecahedron with 20 vertices, 90 edges, and 60 triangular faces.

1 self-dual with 20 vertices, 60 edges, and 20 faces: the ditrigonal icosahedron, being both an icosahedron stellation and a dodecahedron faceting,

3 stellations of the rhombic triacontahedron with 60 vertices, 120 edges, and 30 octagrammic faces, and their duals, which are:

3 facetings of the icosidodecahedron with 30 vertices, 120 edges, and 60 crossed quadrilateral faces.

3 stellations of the rhombic triacontahedron with 120 vertices, 180 edges, and 30 dodecagrammic faces, and their duals, which are:

3 facetings of the icosidodecahedron with 30 vertices, 180 edges, and 120 triangular faces.

3 non-chiral dual pairs with 60 vertices, 150 edges, 60 pentagonal faces,

5 chiral dual pairs with 60 vertices, 150 edges, 60 pentagonal faces,

7 non-chiral dual pairs with 60 vertices, 180 edges, 60 hexagonal faces,

3 non-chiral self-duals with 60 vertices, 180 edges, 60 hexagonal faces,

2 chiral dual pairs with with 60 vertices, 180 edges, 60 hexagonal faces,

2 chiral self-duals with 60 vertices, 180 edges, 60 hexagonal faces.