The compounds of Catalan solids here will be the duals of compound polyhedra made from Archimedean solids. I like to call these "combocatalans".
Trisso - Triakis stella octangula, triakis stellated octahedron
Compound of 2 tikit. Dual of tisso.
Trichi - Triakis chiricosahedron
Compound of 5 tikit. Dual of taki.
Tre - Triakis icosicosahedron
Compound of 10 tikit. Dual of te.
Trissi - Triakis small icosicosahedron
Compound of 5 tikko. Dual of tar.
Re - Rhombic icosicosahedron
Compound of 5 rad. Dual of arie.
Rile - Rhombilanceal icosicosahedron
Compound of 5 sladid. Dual of rasseri.
Pedisi - Pentagonal disicositetrahedron
Compound of 2 pedid. Dual of disco.
Pidis - Pentagonal dishexacontahedron
Compound of 2 sapedit. Dual of dissid.
Tell me if I should rename some and information I should add.
I'm going to try and make pictures of them.