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Difference between revisions of "Octahedral space"

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A space obtained from an [[Octahedron|octahedron]] by identifying its opposite triangular faces, positioned at an angle of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/o/o068/o068090/o0680901.png" /> 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 octahedron 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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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==
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<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>
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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=15819
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article