Use lots of smaller poles and make it really roll like a cylinder.
You'd get into a law of diminishing returns in rolling resistance compared to the complexity of the modification. You could probably turn the octagonal section of the modified (cuboid) block into a dodecagonal section by using rods of two or three different diameters and lashed into (their term) "mats" before being lashed onto the block. But whether it would be as stable, is one very open question ; whether it would be as strong under cornering (which would preferentially load the thinnest rods in the "mat") as the octagonal-section / dodecahedral-enveloped system that is proposed here.
Hmmm, I'm trying to remember my crystallographic space groups. Dodecahedra are in the same space group (class) as cubes (it's the secondary axes of 3-fold rotational symmetry that matter), so by choosing the arrangement of rods in the mat you should be able to make the envelope into a true (Platonic) dodecahedron envelope. Contrary to the paper's illustration, you'd need to attach three trios of "rods" to the three pairs of faces so that the ends of the rods protrude over the faces of the (cubic) core. And you'd need two different lengths of rods, to round off the corners. And I'm falling into exactly the same "diminishing returns" trap that I'm pointing out under your feet.
There's some interesting geometry there. And since I'm sharing an office with a lifting-slinging-hoisting-crane operations instructor, I think I'll shove that paper under his nose because he likes fiddling with scraps of rope (a "marlinspike seaman" as they were called in my youth), and I think he'll be interested.
It's an interesting idea. But it does clearly contradict the evidence of the contemporary records, which is a BIG strike against it being true.