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In [5], Wenninger recommends making polyhedron models as a classroom activity. Among other polyhedra he chooses 15 nonconvex uniform polyhedra. This Demonstration shows 11 of them; five are in Uniform Polyhedron (Wolfram MathWorld). He quotes Coxeter [1]: "The chief reason for studying regular polyhedra is still the same as in the time of the Pythagoreans, namely, that their symmetrical shapes appeal to one's artistic sense."

Coordinates of polyhedra were calculated using [3] and [4].

References

[1] H. S. M. Coxeter, Regular Polytopes, New York: Dover, 1973.

[2] P. R. Cromwell, Polyhedra, New York: Cambridge University Press, 1997.

[3] R. E. Maeder, The Mathematica Programmer II, San Diego: Academic Press, 1996.

[4] R. Webb. "Great Stella." (2014) www.software3d.com/Stella.php.

[5] M. J. Wenninger, Polyhedron Models for the Classroom, Reston, VA: National Council of Teachers of Mathematics, 1975.