Circles of Regular octahedron and Cube

Inversion(Triakis Tetrahedron and Truncated Tetrahedron)

Circles of Catalan solids(Small Rhombicuboctahedron and Deltoidal Icositetrahedron)

Circles of Regular Tetrahedron and Regular Octahedron and Regular Icosahedron

Circles of Catalan solids(Great Rhombicuboctahedron and Disdyakis Dodecahedron)