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 | + | {{TEX|done}} |
| + | 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 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. | ||
Revision as of 16:27, 15 April 2014
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 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.
How to Cite This Entry:
Octahedral space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Octahedral_space&oldid=31753
Octahedral space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Octahedral_space&oldid=31753
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article