Wikipedia on what has been called “the doily” —
“The smallest non-trivial generalized quadrangle
is GQ(2,2), whose representation* has been dubbed
‘the doily’ by Stan Payne in 1973.”
A later publication relates the doily to grids.
From Finite Generalized Quadrangles , by Stanley E. Payne
and J. A. Thas, December 1983, at researchgate.net, pp. 81-82—
“Then the lines … define a 3×3 grid G (i.e. a grid
consisting of 9 points and 6 lines).”
. . . .
“So we have shown that the grid G can completed [sic ]
in a unique way to a grid with 8 lines and 16 points.”
. . . .
“A 4×4 grid defines a linear subspace
of the 2−(64,4,1) design, i.e. a 4×4 grid
together with the affine lines on it is AG(2,4).”
A more graphic approach from this journal —
Click the image for further details.
* This wording implies that GQ(2,2) has a unique
visual representation. It does not. See inscape .