GMR of 6-strand triangular conductor

The GMR (self-GMD for inductance) 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 taken as $r' = 0.7788r$.

            (1)
         (2)   (3)
      (4)   (5)   (6)
   touching strands, centre spacing 2r

The centres lie on a triangular grid of side $2r$. With $r = 1$ cm, $2r = 2$ cm.

Distances (in cm)

Check: 9 + 3 + 3 = 15 pairs $= \binom{6}{2}$.

Product of mutual distances (each pair counted twice):

$$\left[2^9 \times 3.464^3 \times 4^3\right]^2$$

GMR

$$\begin{aligned} D_s &= \left[(r')^6 \times \left(2^9 \times (2\sqrt3)^3 \times 4^3\right)^2\right]^{1/36} \\ r' &= 0.7788 \times 1 = 0.7788\ \text{cm} \\ D_s &= 2.1023\ \text{cm} \end{aligned}$$

Answer: GMR $= 2.102r = 2.102$ cm (for capacitance, with $r$ in place of $r'$, it would be 2.192 cm).