polygonhood

noun1

1. •
   (rare) The state of being a polygon.

   • Richard R. Brockhaus (1991), Pulling up the ladder: the metaphysical roots of Wittgenstein's Tractatus, →ISBN, page 195: “However, the circle lacks an essential property of polygonhood, namely having angles, and thus as a convenient fiction we refer to it as a degenerate case of a polygon.”
   • W.S. Anglin (1997), The Philosophy of Mathematics: the Invisible Art, →ISBN, page 11: “None the less, for any natural number n > 3, there is a form of n-hood, and a form of n-sided polygon-hood. For example, when n = 4, we have the form of fourness and the form of squareness.”