seed=6 NCLIMB=30 n in [5, 8]
tetrahedron: n=4 critical scale=0.99339 connected_grid=True R=1.17312 2*2^(-1/n)=1.68179 1-D check: hull|q_u|=0.3246 beta_u=1.24755 pi(x*)=1.17312
triangular bipyramid: n=5 critical scale=0.98212 connected_grid=True R=1.12470 2*2^(-1/n)=1.74110 1-D check: hull|q_u|=0.1699 beta_u=1.22710 pi(x*)=1.12470
octahedron: n=6 critical scale=0.97209 connected_grid=True R=1.08110 2*2^(-1/n)=1.78180 1-D check: hull|q_u|=0.1250 beta_u=1.19682 pi(x*)=1.08110
pentagonal bipyramid: n=7 critical scale=0.95362 connected_grid=True R=1.05142 2*2^(-1/n)=1.81145 1-D check: hull|q_u|=0.0628 beta_u=1.18654 pi(x*)=1.05142
cube: n=8 critical scale=0.95475 connected_grid=True R=1.03234 2*2^(-1/n)=1.83401 1-D check: hull|q_u|=0.0455 beta_u=1.17671 pi(x*)=1.03234
square antiprism: n=8 critical scale=0.95520 connected_grid=True R=1.03261 2*2^(-1/n)=1.83401 1-D check: hull|q_u|=0.0460 beta_u=1.17742 pi(x*)=1.03261
near-collinear start n=5 sigma=0.02: start R=1.72735 -> 1.73370 after 30 steps (accepted 2); transverse singular values=[0.126 0.015]; 2*2^(-1/n)=1.74110; exceeds it: False
near-collinear start n=5 sigma=0.08: start R=1.68666 -> 1.71261 after 30 steps (accepted 4); transverse singular values=[0.278 0.091]; 2*2^(-1/n)=1.74110; exceeds it: False
near-collinear start n=5 sigma=0.3: start R=1.54291 -> 1.68417 after 30 steps (accepted 15); transverse singular values=[0.459 0.093]; 2*2^(-1/n)=1.74110; exceeds it: False
n=5: best near-collinear/climb R=1.73370 (< 2: True)
near-collinear start n=8 sigma=0.02: start R=1.79312 -> 1.80006 after 30 steps (accepted 1); transverse singular values=[0.15  0.132]; 2*2^(-1/n)=1.83401; exceeds it: False
near-collinear start n=8 sigma=0.08: start R=1.72941 -> 1.76214 after 30 steps (accepted 4); transverse singular values=[0.227 0.209]; 2*2^(-1/n)=1.83401; exceeds it: False
near-collinear start n=8 sigma=0.3: start R=1.19177 -> 1.24564 after 30 steps (accepted 10); transverse singular values=[1.148 0.604]; 2*2^(-1/n)=1.83401; exceeds it: False
n=8: best near-collinear/climb R=1.80006 (< 2: True)
