Keywords: Higman-Sims-01.svg Created with Sage Higman “Sims graph as an orthogonal projection from a subset of the Leech lattice emphasizing a rotational symmetry of order 11 There are 11 possible such projections if we require all 22 points connected to the center point to form a regular 22-gon around it graphe de Higman “Sims comme projection orthogonale d'un sous-ensemble du réseau de Leech mettant en évidence une symétrie rotationnelle d'ordre 11 Il y a 11 telles projections possibles si on impose aux 22 points reliés au point central de former un 22-gone régulier autour de lui own Gro-Tsen 2010-10-30 Source code The following Sage source code can be used to generate the graph data for this file and the similarly named ones the actual SVG files were generated by postprocessing this output with a simple Perl script not listed here <syntaxhighlight lang python >m24 MathieuGroup 24 lst m24 conjugacy_classes_representatives elt x for x in lst if x order 11 0 fixthis Permutation elt fixed_points octad0 Permutation x fixed_points for x in lst if x order 2 and len Permutation x fixed_points 8 0 octads gap Orbit gap m24 octad0 OnSets sage octads22 o for o in octads if fixthis0 in o and fixthis1 in o pointP QQ 24 4 if i+1 in fixthis else 0 for i in range 24 pointsQ QQ 24 -3 if i k else 1 for i in range 24 for k in range 24 if not k+1 in fixthis pointsR QQ 24 2 if i+1 in o else 0 for i in range 24 for o in octads22 hsGraph pointP + pointsQ + pointsR melt elt matrix def sqnorm v return sum x x for x in v adjacency i for i in range i0 if sqnorm hsGraphi-hsGraphi0 48 for i0 in range 100 def chop v if abs v <1 e-9 return 0 return v p sum melt i N exp -2 I i pi/11 for i in range 11 /11 def writeit twist fname v p CC 24 1 if i 0 else N exp twist I pi/11 if i 1 else 0 for i in range 24 va RR 24 vi real for i in range 24 vb RR 24 vi imag for i in range 24 t va norm v / t va / t vb / t coords va pt vb pt for pt in hsGraph fd open fname w for i0 in range 100 for i in adjacencyi0 print >>fd line chop coordsi00 chop coordsi01 chop coordsi0 chop coordsi1 for pt in coords print >>fd point chop pt0 chop pt1 fd close for i in range 1 22 2 writeit i /tmp/hs 02d dat i </syntaxhighlight> Higman-Sims Graph Images with Sage source code |