A complex polytope is a generalization of a polytope which exists in a complex Hilbert space, where each real dimension is accompanied by an imaginary one. The "imaginary" number <math>i</math> is defined as the square root of −1. A complex number, say <math>(a + ib)</math> where <math>a</math> is real and <math>ib</math> is imaginary, lies in a complex plane, which may be represented as a real Argand diagram.

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  • A complex polytope is a generalization of a polytope which exists in a complex Hilbert space, where each real dimension is accompanied by an imaginary one. The "imaginary" number <math>i</math> is defined as the square root of −1. A complex number, say <math>(a + ib)</math> where <math>a</math> is real and <math>ib</math> is imaginary, lies in a complex plane, which may be represented as a real 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 <math>x</math> and <math>y,</math> and two imaginary dimensions <math>ix</math> and <math>iy. </math> (Note however that in the case of polygons, the term 'complex polygon' also has other meanings.)
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  • A complex polytope is a generalization of a polytope which exists in a complex Hilbert space, where each real dimension is accompanied by an imaginary one. The "imaginary" number <math>i</math> is defined as the square root of −1. A complex number, say <math>(a + ib)</math> where <math>a</math> is real and <math>ib</math> is imaginary, lies in a complex plane, which may be represented as a real Argand diagram.
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  • Complex polytope
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