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There are four regular non-convex polyhedra 
known as the Kepler-Poinsot Polyhedra.
http://cage.rug.ac.be/~hs/polyhedra/keplerpoinsot.html 
Two of them were described by Johannes Kepler in 1619 
as being regular. One of them appears on a 16th century 
drawing by Jamnitzer and the another on a 
15th century mosaic, by Paolo Uccello, on the floor of  
San Marco in Venice.
http://www.georgehart.com/virtual-polyhedra/uccello.html
http://math.unipa.it/~grim/SiSala2.PDF 
The other two were described by Louis Poinsot in 1809 
but at least one of them appears on a drawing by the same 
Jamnitzer. In 1810 the French mathematician Augustin-Louis 
Cauchy proved that the five Platonic and the four 
Kepler-Poinsot polyhedra are the only possible regular 
polyhedra.

References:
http://www.arxiv.org/abs/math-ph/0303071