seed=5 NCLIMB=30 n in [4, 6]
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=4 sigma=0.02: start R=1.67998 -> 1.67998 after 30 steps (accepted 0); transverse singular values=[0.059 0.029]; 2*2^(-1/n)=1.68179; exceeds it: False
near-collinear start n=4 sigma=0.08: start R=1.63174 -> 1.65548 after 30 steps (accepted 8); transverse singular values=[0.31  0.071]; 2*2^(-1/n)=1.68179; exceeds it: False
near-collinear start n=4 sigma=0.3: start R=1.42173 -> 1.56895 after 30 steps (accepted 13); transverse singular values=[0.624 0.29 ]; 2*2^(-1/n)=1.68179; exceeds it: False
n=4: best near-collinear/climb R=1.67998 (< 2: True)
near-collinear start n=6 sigma=0.02: start R=1.77869 -> 1.77869 after 30 steps (accepted 0); transverse singular values=[0.07  0.018]; 2*2^(-1/n)=1.78180; exceeds it: False
near-collinear start n=6 sigma=0.08: start R=1.70714 -> 1.72122 after 30 steps (accepted 5); transverse singular values=[0.289 0.167]; 2*2^(-1/n)=1.78180; exceeds it: False
near-collinear start n=6 sigma=0.3: start R=1.41468 -> 1.54214 after 30 steps (accepted 11); transverse singular values=[0.81  0.266]; 2*2^(-1/n)=1.78180; exceeds it: False
n=6: best near-collinear/climb R=1.77869 (< 2: True)
