English: Rectangles in aspect ratios ${\displaystyle (\varsigma -1{)}^{\pm 1}}$ (blue, green), ${\displaystyle \frac{\varsigma }{\varsigma -1}}$ (red, brown) and ${\displaystyle \varsigma }$ (purple, yellow) tile the square, with supersilver ratio ${\displaystyle \varsigma }$ the real root of ${\displaystyle x^3=2x^2+1.}$
The supersilver ratio ${\displaystyle \varsigma }$ and tribonacci constant ${\displaystyle \tau }$ have approximate relation ${\displaystyle \frac{1}{\varsigma -1}\approx \tau -(1+\frac{1}{102}).}$ Thus, with the appropriate swaps of rectangle ratios (${\displaystyle \varsigma \approx \frac{\tau }{\tau -1},}$ and vice versa), the tiling diagrams are almost identical: