= Square lamina
= Hollow square lamina
{synonym}
A <square lamina> is a frame obtained by removing a concentric <square> hole from a larger <square>, \b[with corresponding sides parallel]. If their side lengths are $a>b>0$, the uniform border thickness is $t=(a-b)/2$ and the frame has <area>
$$
a^2-b^2=(a-b)(a+b)=4t(b+t).
$$
For <positive integer> sides $a,b$ with the same <integer parity>, $t$ is a <positive integer>, and a unit-grid frame contains exactly $4t(b+t)$ <unit squares>. For example, outer side five and inner side three give thickness one and sixteen <unit squares>. Concentricity alone would allow a rotated inner <square>; the parallel-side condition is what makes this a uniform lattice border.
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