The first example of a Poincaré space. Constructed by H. Poincaré in 1904. It is obtained by identifying the opposite faces of a dodecahedron after they have been rotated by an angle $\pi\over 5$ relative to each other. The dodecahedral space is a manifold of genus 2 with a Seifert fibration and is the only known Poincaré space with finite fundamental group. A dodecahedral space is the orbit space of the free action of a binary icosahedron group on the three-dimensional sphere.
|||H. Seifert, W. Threlfall, "Lehrbuch der Topologie" , Chelsea, reprint (1980)|
Dodecahedral space. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Dodecahedral_space&oldid=21691