Difference between revisions of "Dodecahedral space"
From Encyclopedia of Mathematics
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| − | The first example of a [[ | + | 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==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> H. Seifert, W. Threlfall, "Lehrbuch der Topologie" , Chelsea, reprint (1980)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> H. Seifert, W. Threlfall, "Lehrbuch der Topologie" , Chelsea, reprint (1980)</TD></TR></table> | ||
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| + | ====Comments==== | ||
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| + | ====References==== | ||
| + | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> José Maria Montesinos, "Classical tessellations and three-manifolds" Springer (1987) ISBN 3-540-15291-1 {{ZBL|0626.57002}}</TD></TR></table> | ||
Revision as of 15:37, 19 January 2021
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) |
Comments
References
| [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=51425
Dodecahedral space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dodecahedral_space&oldid=51425
This article was adapted from an original article by A.V. Chernavskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article