Inspired by their work, Thurston took a different, more explicit means of exhibiting the hyperbolic structure of the figure-eight knot complement. He showed that the figure-eight knot complement could be decomposed as the union of two regular ideal hyperbolic tetrahedra whose hyperbolic structures matched up correctly and gave the hyperbolic structure on the figure-eight knot complement. By utilizing Haken's normal surface techniques, he classified the incompressible surfaces in the knot complement. Together with his analysis of deformations of hyperbolic structures, he concluded that all but 10 Dehn surgeries on the figure-eight knot resulted in irreducible, non-Haken non-Seifert-fibered 3-manifolds. These were the first such examples; previously it had been believed that except for certain Seifert fiber spaces, all irreducible 3-manifolds were Haken. These examples were actually hyperbolic and motivated his next theorem.