The oct family: the unit net subdivided by a + bω
(T = a²+ab+b²), every lattice point a genuine net, drawn with its
mirror sector below the axis. Reflections are lumped, so the two
half-sectors show the same nets; for a chiral unit they would be
distinct. Solid dots are built (click to open); pale dots are not
built yet. T is not injective: e.g. (7,0) and (5,3) are different nets
with T = 49. Subdivisions are computed with
Antiprism (Adrian Rossiter’s
geodesic).