He is the namesake of the Hurwitz surface of the lowest possible genus, a compact Riemann surface of genus three and order 168, known as his eponymous quartic. This author of the influential classification scheme set forth in the Erlangen Program is the namesake of a (*) disc model of the hyperbolic plane in which a line is defined as a chord. His namesake group has four elements and is the smallest non-cyclic group. A surface named for this man is the only exception to the Heawood conjecture, being non-orientable like the Mobius strip. For 10 
He is the namesake of the Hurwitz surface of the lowest possible genus, a compact Riemann surface of genus three and order 168, known as his eponymous quartic. This author of the influential classification scheme set forth in the Erlangen Program is the namesake of a (*) disc model of the hyperbolic plane in which a line is defined as a chord. His namesake group has four elements and is the smallest non-cyclic group. A surface named for this man is the only exception to the Heawood conjecture, being non-orientable like the Mobius strip. For 10 points, name this man, the namesake of a closed, two-dimensional manifold, his eponymous "bottle."
He is the namesake of the Hurwitz surface of the lowest possible genus, a compact Riemann surface of genus three and order 168, known as his eponymous quartic.
Felix {Klein}