The 110 faces are:

• sixty irregular pentagons
• thirty elongated, irregular hexagons
• twenty hexagons which are equiangular, and nearly equilateral as well

Created using Stella 4d, available at http://www.software3d.com/stella.php.

The 242 faces are:

• sixty irregular heptagons
• sixty rectangles
• sixty isosceles trapezoids
• thirty irregular octagons
• twenty hexagons which are equiangular but not quite equilateral
• twelve regular pentagons

Created using Stella 4d, available at http://www.software3d.com/Stella.php.

The 132 faces are:

• sixty isosceles triangles, in 30 pairs with common bases
• twelve regular pentagons
• sixty isosceles triangles with bases on the sides of each pentagon

This polyhedron is the dual of the one in the previous post.

Created using Stella 4d, available at http://www.software3d.com/stella.php.

The eighty faces are:

• twenty hexagons which are equilateral, but not equiangular
• sixty irregular pentagons

Created using Stella 4d, available at http://www.software3d.com/stella.php.

The faces are:

• twelve irregular decagons
• twenty irregular nonagons
• sixty irregular pentagons
• sixty isosceles trapezoids

This polyhedron was created using Stella 4d, which may be tried for free at http://www.software3d.com/stella.php.