 | This article has problems which may render some text or images unreadable or difficult to read in dark mode. Desktop readers can switch to light mode temporarily using the eyeglasses icon at the top of the page. (September 2024) |
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 regular complex polytopes, which are configurations. The regular complex polytopes have been completely characterized, and can be described using a symbolic notation developed by Coxeter.
Some complex polytopes which are not fully regular have also been described.