GMR of 4-strand conductor in terms of r

The GMR of an $n$-strand conductor is the $n^2$-th root of the product of all inter-strand distances, with each strand's self-distance $r' = 0.7788r$.

     (1)   (2)
     (3)   (4)
  side = 2r, diagonal = 2(sqrt2)r

Distances

By symmetry every strand sees the same set: $r'$, $2r$, $2r$, $2\sqrt2 r$.

GMR

$$\begin{aligned} D_s &= \left[(r' \cdot 2r \cdot 2r \cdot 2\sqrt2 r)^4\right]^{1/16} = \left(r' \times 8\sqrt2\, r^3\right)^{1/4} \\ &= \left(0.7788 \times 11.314\right)^{1/4} r = (8.811)^{1/4} r \\ &= 1.7229\,r \end{aligned}$$

Answer: GMR $= 1.723r$ (for capacitance, using $r$ instead of $r'$, it is $1.834r$).