There are, as faces, 24 irregular heptagons, 6 irregular octagons of one type, and 12 of another, 24 rectangles of one type, and 24 of another, and 8 equilateral triangles. This was made using Stella 4d, which you may try or buy at http://www.software3d.com/Stella.php.
The great icosahedron has 20 faces which are interpenetrating equilateral triangles, most of which are hidden in the interior of that polyhedron. The non-hidden, and therefore visible, parts are called “facelets” — and there are 180 of them: 120 scalene, and 60 isosceles.
In this variant of the great icosahedron, the sixty isosceles facelets are simply missing, which changes the shape of the remaining 120, still-scalene facelets. The color scheme is one which gives each facelet a different color — except for coplanar or parallel facelets, which are the same color, making them easier to spot.
Software credit: see http://www.software3d.com/stella.php — with a free trial download available there.
RobertLovesPi.net 