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.
RobertLovesPi.net 
Robert – you seem to have made some complex models using a lot of peculiar shapes and yet the 4pentagon/4trapezoid solid was problematic? Please explain.
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In this particular case, if I recall correctly, I used a lot of augmentation and the creation of convex hulls to produce this polyhedron. The 4 pentagon / 4 trapezoid solid was difficult because Stella was not set up with it in mind — I think. Stella won’t allow you to simply input a net, and give you a polyhedron as output, but it does allow a great many different transformations to be made on a large number of possible starting polyhedra.
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Hi!
I’ve been working on a modified Hexakis Icosahedron to get a polyhedron with 242 vertices. It looks like the dual to your polyhedron here.
It has 480 faces and 720 edges.
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