Dodecahedral space

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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 $\frac \pi 5$ 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.


[1] H. Seifert, W. Threlfall, "Lehrbuch der Topologie" , Chelsea, reprint (1980)
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Dodecahedral space. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.V. Chernavskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article