Bianchi Orbifolds

Shown below are pictures of the 3-dimensional orbifolds which are the quotient of hyperbolic 3-space by the Bianchi group PGL(2,O) where O is the ring of integers in the imaginary quadratic field of discriminant D=-3, -4, -7, -8, -11, -15, -19, -20, -23, -24, -31, -35, -39, -47, -51, -56, -59, -68, -71. In each of these cases the orbifold is topologically the 3-sphere with punctures (shown as tiny circles), and the pictures show the singular locus of the orbifold structure.

For more details see "Bianchi Orbifolds of Small Discriminant," a brief unpublished report I wrote in 1983, available electronically as a pdf file (95K, 6 pages).