I found this 4D vertex configuration, with 2 each of n-gon prisms, trigonal prisms, pentagonal prisms, and pentagonal pyramids. Each edge is surrounded by 4 polyhedra, so we can't easily calculate the dichoral angles.

I have numerically calculated the dichoral angle between the two n-gon prisms:

n=3: 167.093891°

n=4: 166.559686°

n=5: 165.732024°

n=6: arccos((1 - 3φ)/4) = 164.48°

n=7: 162.505191°

n=8: 159.162429°

n=9: no convex solution

n≥10: dihedral angle sum exceeds 360°

From this we can get the other dichoral angles. They are all less than 180°. In the case n=6, I recognized some of the angles, and thereby derived the exact algebraic value given above; the angle between 'trip' and 'peppy' is 150°, and the angle between 'pip' and 'peppy' is 162°. In the other cases, none of the dichoral angles were found in the list of CRF polyhedron dihedral angles.

It remains to be seen whether this can be part of a CRF polychoron.