Namespaces
Variants
Actions

Dodecahedral space

From Encyclopedia of Mathematics
Jump to: navigation, search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

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 the binary icosahedral group on the three-dimensional sphere.

References

[1] H. Seifert, W. Threlfall, "Lehrbuch der Topologie" , Chelsea, reprint (1980)
[a1] José Maria Montesinos, "Classical tessellations and three-manifolds" Springer (1987) ISBN 3-540-15291-1 Zbl 0626.57002
How to Cite This Entry:
Dodecahedral space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dodecahedral_space&oldid=53740
This article was adapted from an original article by A.V. Chernavskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article