Published July 24, 2024 | Version V1
Software Open

Generator of maximally connected polyhedral cages

  • 1. University of Durham

Description

bi_sym_cages_56 optimizes a p-cage for a set of parameter using a simulated annealing method.. One must select the type of p-cage ( HAP6 TTP6 TOP6 PD
IP5 SDP5 TCM4 TOM3 TTM3), the two polygon size P1 and P2 (both at least 6), the number of hole-edges, qs and Qs as a list of coma separated integers satisfying the constraints P1-5 = a+b+c+d+e, P2-6=A+B+C+D+E+F.

The remaining parameters control the optimisation. cl and ca are the weight for the regularity optimisation. If N_cl_ca/ncla is positive, typically 100, the program tries 200 values of cl and ca with the constraints that cl+ca=2, scanning the values on a logarithmic progression. If ncla<=0 only the specified values of cl and ca are used.

The python program mk_all_cages.py creates a script file for every a-e, A-F parameter for a given p-cage type.

bi_sym_cages_56 -P1 N -P2 N -q1 N -q2 N -q3 N  [-q4 N] [-q5 N]  [-T0 R] [-Tmin R] [-n_sweep N] [-n_monitor N]

EXAMPLE (with a good set of parameter values for the optimisation):

bi_sym_cages_56 -type SDP5 -P1 15 -P2 20 -qs 2,2,2,2,2 -Qs 2,2,3,2,2,3 -S1 1 -S2 1  -cc 10000 -cpc 10000 -T0 4e-5 -Tmin 1e-8 -track 500 -n_sweep 2000 -nr 10 -ncla 100 -dx_min 1e-13 -use_grad_mc -cla_mc -pure_mc

 

 

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Additional details

Related works

Is supplement to
Journal article: 10.3390/sym17010101 (DOI)

Funding

Leverhulme Trust
Cages with Paradoxical Geometries RPG-2020-306