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About: Complex polytope     Goto   Sponge   NotDistinct   Permalink

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In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one. A complex polytope may be understood as a collection of complex points, lines, planes, and so on, where every point is the junction of multiple lines, every line of multiple planes, and so on. Precise definitions exist only for the , which are configurations. The regular complex polytopes have been completely characterized, and can be described using a symbolic notation developed by Coxeter.