Octahedral space
From Encyclopedia of Mathematics
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