A polytope constructed in such a unitary space is called a "'complex polytope " '.
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Inner product spaces over the field of complex numbers are sometimes referred to as "'unitary spaces . "'
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(Here, a flat of dimension " 1 is taken to mean the empty set . ) Thus, by definition, regular complex polytopes are configurations in complex unitary space.
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The first complete mathematical formulation of this approach, known as the Dirac von Neumann axioms, is generally credited to John von Neumann's 1932 book " Mathematical Foundations of Quantum Mechanics ", although Hermann Weyl had already referred to Hilbert spaces ( which he called " unitary spaces " ) in his 1927 classic paper and book.
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