This work belongs to Indiana's 1962 Polygon series, small paintings featuring a numeral from 3 to 12 placed inside a polygon of the corresponding number of sides (i.e. 3-Triangle, 4-Square, etc.). The series features extensive wordplay, with references that are playful, personal, literary, and alliterative.
Polygon: Square is one of two works with the same title (see Polygon: Square). In both examples the same pair of words appear within the circle but with a notable exception—in this painting Indiana writes “Quare Quadrangel” and in the second canvas “Quare Quadrangle." The artist's journal entry for June 16, 1962, indicates that "quadrangel" was an unintended misspelling, hence he created a second painting.
The word "quare” references Brendan Behan's 1954 The Quare Fellow, a play about the death penalty, set in Mountjoy Prison in Dublin (the Irish connection emphasized by the work's palette of orange, green, and white). Behan's play opens with the song “The Auld Triangle” whose chorus, “Oh the jingle jangle of the auld triangle,” may have suggested the rhyme of triangle and “Quadrangel/Quadrangle.” Indiana would also have delighted in the reduction of “square” to “quare,” as shortening words and playing with their meaning was a regular feature of his work. Two other examples of such wordplay are the painting For (shortened from the word “fork”) and the sculpture Bar (shortened from “Barr,” a reference to Alfred H. Barr, Jr. of the Museum of Modern Art, New York).