Snub dodecahedron
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The Snub dodecahedron has 92 faces (12 pentagons, 80 equilateral triangles), 150 edges, and 60 vertices.
I will be re-looking at the procedure for this at a later date. I have either miscalculated an angle somewhere (I do not believe that this is the case as I would have noticed edges not meeting properly earlier) but when I went to start the last round of equilateral triangles, they were not lining up correctly.
despite not being complete, I still believe it is an interesting item to view.
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It is absolutely interesting to see. :-) We can see the inside of this Snub Dodecahedron.
More info: http://en.wikipedia.org/wiki/Snub_dodecahedron