View source for Octahedral space

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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 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.