The designation F-4H was not applied, lest it be confused with the
pre-1962 designation of F4H for the Phantom.
Sources:
-
McDonnell Douglas Aircraft Since 1920: Volume II, Rene J.
Francillon, Naval Institute Press, 1990.
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McDonnell F-4 Phantom: Spirit in the Skies. Airtime Publishing, 1992.
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The American Fighter, Enzo Angelucci and Peter Bowers, Orion, 1987.