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Complex polytope
From Wikipedia, the free encyclopedia
A complex polytope is one which exists in a unitary space, where each real dimension is accompanied by an imaginary one.
A complex number, say (a + ib) lies in a complex plane, which may be represented as an Argand diagram. An n-dimensional unitary space comprises n such complex planes, all orthogonal to each other.
For example a complex polygon exists in the unitary plane of two real dimensions x and y, and two imaginary dimensions ix and iy. (Note however that in the case of polygons, the term 'complex polygon' also has other meanings.)
In the ordinary, or real plane, we can construct a visible figure as the real conjugate of some complex polygon. Likewise in ordinary space, we can construct a visible figure as the real conjugate of some complex polyhedron.
- Coxeter, H. S. M., Regular Complex Polytopes, Cambridge University Press, 1974.
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