Difference between revisions of "Octahedral space"
From Encyclopedia of Mathematics
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| − | A space obtained from an [[Octahedron|octahedron]] by identifying its opposite triangular faces, positioned at an angle of $\pi/3$ to each other. An octahedral space is a [[Three-dimensional manifold|three-dimensional manifold]] and is the orbit space of the action of a binary | + | A space obtained from an [[Octahedron|octahedron]] by identifying its opposite triangular faces, positioned at an angle of $\pi/3$ to each other. An octahedral space is a [[Three-dimensional manifold|three-dimensional manifold]] and is the orbit space of the action of a [[binary octahedral group]] on a three-dimensional sphere. It can be identified with a cube space obtained in an analogous way. The one-dimensional Betti group of an octahedral space is a group of order three. |
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| + | ==References== | ||
| + | <table> | ||
| + | <TR><TD valign="top">[1]</TD> <TD valign="top"> H.S.M. Coxeter, "Regular complex polytopes" , Cambridge Univ. Press (1991) {{ZBL|0732.51002}}</TD></TR> | ||
| + | </table> | ||
Latest revision as of 15:42, 19 January 2021
A space obtained from an octahedron by identifying its opposite triangular faces, positioned at an angle of $\pi/3$ to each other. An octahedral space is a three-dimensional manifold and is the orbit space of the action of a binary octahedral group on a three-dimensional sphere. It can be identified with a cube space obtained in an analogous way. The one-dimensional Betti group of an octahedral space is a group of order three.
References
| [1] | H.S.M. Coxeter, "Regular complex polytopes" , Cambridge Univ. Press (1991) Zbl 0732.51002 |
How to Cite This Entry:
Octahedral space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Octahedral_space&oldid=51430
Octahedral space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Octahedral_space&oldid=51430
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article