Since stating that no cubic piece has a SOLL of either 7 or its multiple by
9, 63, I have noticed something further: no cubic piece has a SOLL one
short of a multiple of 8 full stop. Geometries with a hex component have a
monopoly over the Sennight and Foal (7), Mountie (15), Germinator and
Hybridiser (23), Newlywed and Vampire (31, perhaps the oddest juxtaposition
of same-SOLL piece names), Barnowl (39), Tesselator (47), Drudge (55), and
Mede (79). As orthogonal leapers' SOLLs always divide by 8 with remainder
0, 1, or 4 it follows that square-cell leapers' SOLLs generally always
divide by 8 whose remainder is a sum of two of those modulo 8: 0, 1, 2, 4,
or 5 - and likewise cubic ones a sum of three of them modulo 8: 0, 1, 2, 3,
4, 5, or 6.
