[CROSS a.] The corner of a quadrilateral diagonally opposite to another. At cross-corners with: fig. directly opposite or contrary to. Hence (nonce-wd.) Cross-cornerness.
180912. Mar. Edgeworth, Absentee, ix. Set the sea-cale at this corner, and put down the grass cross-corners.
1892. Mrs. Lynn Linton, in New Review, Feb., 225. Private idiosyncrasies which place them at cross-corners with the rest of their race.
1884. Illustr. Lond. News, 10 May, 442/2. Pondering on the cross-cornerness of things in general.