This displays a 62 circle packing created by Sam Corvino. It is based on a {5 3 2} 'Schwarz Triangle'; 120 of these tile the sphere and carry arcs of circles along to form the packing. A {5 3 2} Schwarz triangle is one having angles pi/5, pi/3, and pi/2. One of these triangles can propogate by repeated reflection across edges until 120 of them exactly tile the sphere. Packing p0 illustrates a maximal packing based on this tiling, color coded to reflect their degrees, namely 10, 6, and 4. act 0;cleanse;infile_read Sams532branched.p;cleanse -p1;copy 1;max_pack;NSpole;color -c d;set_disp_text -w -cf;disp -w -cf; The next command shows a branched packing with the same combinatorics. Simple branching occurs at each of the 12 yellow circles. Note the underlying 'dodencahedral' symmetry: the yellow circles are centered at the vertices of a regular dodecahedron in both packings (though the center points are shuffled between the two packings). act 1;color -c d;set_disp_text -w -c -cf {c:d.ne.6};disp -w -C -cf {c:d.ne.6}; In side-by-side windows we show one of the {5 3 2} Schwarz triangles in p0, and the correponding {5/2 3 2} Schwarz triangle in p1. The latter is made of 7 copies of the former (you might try working out the pattern), so the 120 of this larger Schwarz triangle in p1 must cover the sphere 7 times. Click the middle button on faces around the yellow circle in p0 to see the correponding faces wrap twice around in p1. act 0;set_Vlist 10 32 61;set_Flist 92;set_disp_text -w -cf Vlist -f Flist;disp -w -cf Vlist -f Flist;set_disp_text -p1 -w -cf Vlist -f Flist;disp -p1 -w -cf Vlist -f Flist;Map 0 1 disp -p1 -w -cf {c:d.eq.4} disp -p1 -w -cf {c:d.eq.6} disp -p1 -w -cf {c:d.eq.10} NODECOUNT: 62 GEOMETRY: spherical ALPHA/BETA/GAMMA: 1 0 54 PACKNAME: Sams532.p FLOWERS: 1 10 54 25 40 13 33 14 41 23 53 24 54 2 10 55 26 56 27 39 15 34 13 40 25 55 3 10 13 34 15 36 17 37 16 35 14 33 13 4 10 41 14 35 16 42 31 61 32 62 23 41 5 10 39 27 57 28 58 29 38 17 36 15 39 6 10 37 17 38 29 59 30 60 31 42 16 37 7 10 53 23 62 32 45 20 44 18 43 24 53 8 10 54 24 43 18 46 19 47 26 55 25 54 9 10 18 44 20 49 21 50 22 48 19 46 18 10 10 45 32 61 31 60 30 51 21 49 20 45 11 10 47 19 48 22 52 28 57 27 56 26 47 12 10 21 51 30 59 29 58 28 52 22 50 21 13 6 40 2 34 3 33 1 40 14 6 1 33 3 35 4 41 1 15 6 2 39 5 36 3 34 2 16 6 35 3 37 6 42 4 35 17 6 36 5 38 6 37 3 36 18 6 43 7 44 9 46 8 43 19 6 8 46 9 48 11 47 8 20 6 7 45 10 49 9 44 7 21 6 50 9 49 10 51 12 50 22 6 52 11 48 9 50 12 52 23 6 7 53 1 41 4 62 7 24 6 43 8 54 1 53 7 43 25 6 8 55 2 40 1 54 8 26 6 8 47 11 56 2 55 8 27 6 11 57 5 39 2 56 11 28 6 58 5 57 11 52 12 58 29 6 59 6 38 5 58 12 59 30 6 51 10 60 6 59 12 51 31 6 10 61 4 42 6 60 10 32 6 45 7 62 4 61 10 45 33 4 1 13 3 14 1 34 4 2 15 3 13 2 35 4 14 3 16 4 14 36 4 15 5 17 3 15 37 4 3 17 6 16 3 38 4 5 29 6 17 5 39 4 2 27 5 15 2 40 4 25 2 13 1 25 41 4 1 14 4 23 1 42 4 4 16 6 31 4 43 4 24 7 18 8 24 44 4 18 7 20 9 18 45 4 7 32 10 20 7 46 4 8 18 9 19 8 47 4 8 19 11 26 8 48 4 19 9 22 11 19 49 4 9 20 10 21 9 50 4 22 9 21 12 22 51 4 21 10 30 12 21 52 4 28 11 22 12 28 53 4 7 24 1 23 7 54 4 8 25 1 24 8 55 4 8 26 2 25 8 56 4 11 27 2 26 11 57 4 11 28 5 27 11 58 4 29 5 28 12 29 59 4 30 6 29 12 30 60 4 10 31 6 30 10 61 4 10 32 4 31 10 62 4 7 23 4 32 7 RADII: 5.966876326e-01 5.966876326e-01 5.966876326e-01 5.966876326e-01 5.966876326e-01 5.966876326e-01 5.966876326e-01 5.966876326e-01 5.966876326e-01 5.966876326e-01 5.966876326e-01 5.966876326e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 7.853981634e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 4.205343354e-01 CENTERS: 0.0000000000e+00 0.0000000000e+00 2.5132741232e+00 2.0344439358e+00 -1.2566370609e+00 2.0344439359e+00 1.2566370621e+00 2.0344439359e+00 6.2831853109e-01 1.1071487174e+00 -3.1415926530e+00 1.1071487177e+00 -2.5132741231e+00 2.0344439359e+00 2.4027104400e-10 2.0344439360e+00 1.8849555924e+00 1.1071487177e+00 -9.2789706939e-01 1.0162268196e+00 -1.8849555918e+00 1.1071487176e+00 -5.5379129201e-01 NaN -2.5132741224e+00 1.3820857960e+00 7.3034556181e-10 1.3820857960e+00 6.2831853119e-01 2.4892345136e+00 -3.1415926530e+00 2.4892345136e+00 -1.2566370617e+00 6.5235813987e-01 1.8849555922e+00 2.4892345133e+00 8.3592113111e-10 6.5235813986e-01 -2.5132741220e+00 6.5235813965e-01 -8.9261165742e-01 1.2295517547e+00 2.4418356226e-10 1.7595068578e+00 2.5132741233e+00 1.3820857960e+00 -1.2566370615e+00 1.3820857962e+00 1.2566370616e+00 1.3820857960e+00 -1.8849555921e+00 2.4892345136e+00 2.5132741231e+00 6.5235813979e-01 -6.2831853038e-01 1.7595068577e+00 1.8849555926e+00 1.7595068577e+00 -1.9753292362e+00 1.7560896989e+00 1.2566370612e+00 6.5235813985e-01 -6.2831853033e-01 2.4892345137e+00 -1.2566370609e+00 1.0172219680e+00 -2.5132741223e+00 2.5880182948e+00 9.7876855517e-10 2.5880182948e+00 -3.1415926489e-01 1.5707963265e+00 -2.1991148571e+00 1.5707963269e+00 1.8849555933e+00 5.5357435893e-01 1.5707963272e+00 1.5707963265e+00 2.5132741232e+00 1.0172219680e+00 1.2566370623e+00 1.0172219680e+00 2.1991148581e+00 1.5707963265e+00 -1.2566370617e+00 2.5880182951e+00 2.8274333882e+00 1.5707963263e+00 -1.5707963267e+00 1.5707963270e+00 9.4247779636e-01 1.5707963268e+00 -9.4247779579e-01 1.5707963266e+00 3.1415926535e+00 5.5357435901e-01 6.2831853063e-01 5.5357435926e-01 1.6934601868e-01 5.6159662207e-01 NaN NaN -1.2845787595e+00 1.2205884310e+00 -2.5132741229e+00 1.0172219681e+00 0.0000000000e+00 1.0172219680e+00 1.2566370622e+00 2.5880182948e+00 -2.8274333880e+00 1.5707963264e+00 -6.2831853050e-01 5.5357435893e-01 6.2831853116e-01 2.1243706855e+00 -3.1415926528e+00 2.1243706857e+00 -1.8849555911e+00 5.5357435895e-01 3.1415926577e-01 1.5707963270e+00 2.5132741230e+00 2.5880182947e+00 END