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Math for the people, by the people.

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Phrase "is the regular 4-gon, that is," is not a part of definition.
It is a part of properties.
And url of "regular" is inapropriate.
This phrase should be just removed from definition as quadrilateral is enough.
It should be good also to cite Euclid, Book I, Definitions item 22:
a right-angled equilateral quadrilateral figure

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