# TO COMPILE make should compile the program bi_sym_cages and equigraphs_bi_12_snapshot ############################################################### # bi_sym_cages USAGE ############################################################### Example: bi_sym_cages -type Ato -P1 9 -P2 11 -q1 1 -q2 3 -q3 2 -Q1 3 -Q2 1 -Q3 4 -ts 1.1 -S1 1.35 -S2 1.35 -cc 500 -cpc 500 -T0 4e-3 -Tmin 1e-8 -track 500 -n_sweep 1000 -nr 10 -ncla 100 -dx_min 1e-13 -use_grad_mc -cla_mc -pure_mc Find p-cages for 200 values of cl and ca such that c_l+c_a =2 -type TYPE : the type of solid as listed below -P1 9 : use nanogons -P2 11 : and hendecagons -qi : the value of each qi for the nanogons -Qi : the value of each qi for the hendecagons -cc 500 : Face convexity weight for the face. Keep as is -cc 500 : p-cage convexity weight for the face. Keep as is -T0 0.004 : Initial MC temperature. Can require tweaking -Tmin 1e-8 : Minimum MC temperature. -track 500 : MC parameter. -n_sweep 1000 : MC parameter. Keep or increase -nr 10 : preform 10 full relaxation and keep next value. -ncla 100 : number of ca values between 1 and 0.001 and then cl between 1 and 0.001. SO 200 values in total. -dx_min 1e-13 : leave as is -use_grad_mc : use gradient MC -cla_mc : relax each value of cl, ca using MC -pure_mc : use pure MC SOLID TYPE Square Prism (cube) sp Truncated octahedron Ato Truncated cuboctahedron Atco Icosidodecahedron Atid Rhombic dodecahedron DArd Rhombic triacontahedron DArt The program generates text files with the coordinates of the data. ############################################################### # equigraphs_bi_12_snapshot USAGE ############################################################### Generates a list of all potential graphs with two types of vertices such that all the vertices of a given type are equivalent to each other via an automorphism of the graph and such that vertices of a given type are only connected to vertices of the other type. Parameters: P : The maximum size for the faces of the graph L1 : the valence of the 1st type of vertices L2 : the valence of the 2nd type of vertices Fmax : the maximum number of face in the graph. napshot_interval : intervals between snapshots restore : use the specified snapshot file to resume the computation. The output file contains one possible graph per line. Each line is made out of 5 groups separated by ";" and a last one after a "#". 1: L1 L2 2: Coma separated list of "N n1 n2", graph containing N faces with n1 vertices of type 1 and n2 vertices of type 2. 3: Coma separated list of "N n" each vertex of type 1 belongs to N faces of type n as listed in the 2nd group (n starts from 0) 4: Same as 3 but for vertices of type 2. 5: N1 N2 : N1 vertices of type 1 and N2 vertices of type 2 6 : The number after the # is the total number of faces in the graph. Example : equigraphs_bi_12_snapshot -P 10 -L1 3 -L2 4 -Fmax 100 equigraphs_bi_12_snapshot -P 10 -L1 3 -L2 4 -Fmax 100 ############################################################### # PYTHON FILES ############################################################### The folder python contains 2 python programs: ############################################################### # GENERATING off FILES : p_cage_off.py ############################################################### The program p_cage_off.py to converts the coordinates file generated by bi_sym_cages to an off file: bi_p_cage_off.py FILE.txt The "off" files can be viewed with antiview or geomview ############################################################### # GENERATING ALL THE CAGES: mk_all_cages.py ############################################################### One can generate all the potential p-cages of a given type and P-gone using the python program mk_all_cages.py The syntax is mk_all_cages.py -P1=p -P2=p -t=TYPE -qmax=5 -dqmax=5 where p is the number of edges for each polygon t is sp Ato Atco Atid DArd or DArt as in the table above. -qmax is the largest value for the qs. -dqmax is the largest value difference between the qs. The program creates a directory for each p-cage as well as a shell file named "run.csh", in that directory, with the parameters set for that p-cage. The relaxation parameters sometimes have to be tweaked for some p-cages. The shell file "run.csh" can be used to executes bi_sym_cages with the selected parameters. Example All square prism p-cages with octagonal and nonagonal faces mk_all_cages.py -P1=8 -P2=9 -t=sp -qmax=5 -dqmax=5 All truncated octagonal p-cages with hexagonal and decagonal faces mk_all_cages.py -P1=6 -P2=10 -t=Ato -qmax=5 -dqmax=5 All truncated cuboctahedron p-cages with decagonal and ddoecagonal faces mk_all_cages.py -P1=10 -P2=11 -t=Atco -qmax=5 -dqmax=5 All icosidodecagonal p-cages with nonagonal and hendecagonal faces mk_all_cages.py -P1=9 -P2=11 -t=Atid -qmax=5 -dqmax=5