% BCK classification of Archimedean maps of genus 4 % Jan Karabas, Wed Sep 8 11:16:20 CEST 2010 % % DESCRIPTION: % % Map code - see the classification at http://www.savbb.sk/~karabas/science.html#arch % Aut+(M), Aut(M) - the code of the group in SmallGroup Library, use e.g. SmallGroup(n,k) for in GAP % summarized results for classes are below the list Map code Aut+(M) Aut(M) |V| |D| class --------------------------------------------------------------------- A4.1 <72, 42> <144, 183> 144 432 perfect A4.7 <120, 34> <240, 189> 240 720 perfect A4.10 <72, 40> <144, 186> 144 432 perfect A4.16 <40, 8> <80, 39> 80 240 perfect A4.31 <120, 34> <240, 189> 120 360 accurate A4.44 <72, 40> <144, 186> 72 216 accurate A4.46 <36, 12> <72, 46> 72 216 perfect A4.100 <120, 34> <240, 189> 120 360 accurate A4.103 <60, 5> <120, 35> 60 180 accurate A4.105 <72, 42> <144, 183> 72 216 accurate A4.143 <72, 40> <144, 186> 72 216 accurate A4.161 <24, 12> <48, 48> 48 144 perfect A4.163 <72, 42> <144, 183> 72 288 accurate A4.179 <36, 11> <72, 43> 36 144 accurate A4.186 <18, 3> <36, 12> 36 144 perfect A4.205 <120, 34> <240, 189> 120 480 accurate A4.209 <72, 40> <144, 186> 72 288 accurate A4.211 <36, 10> <72, 40> 72 288 perfect A4.213 <36, 10> <72, 46> 72 288 perfect A4.247 <24, 12> <48, 48> 48 192 perfect A4.253 <24, 12> <48, 48> 48 192 perfect A4.254 <24, 12> <48, 48> 48 192 perfect A4.259 <40, 8> <80, 39> 40 160 accurate A4.279 <20, 4> <40, 13> 40 160 perfect A4.286 <20, 3> <40, 12> 40 160 perfect A4.329 <20, 4> <40, 6> 40 160 perfect A4.353 <36, 10> <72, 46> 36 144 accurate A4.356 <36, 10> <72, 46> 36 144 accurate A4.357 <18, 3> <36, 10> 36 144 perfect A4.419 <18, 3> <36, 10> 36 144 perfect A4.515 <24, 12> <24, 12> 24 96 accurate A4.517 <24, 12> <48, 48> 24 96 accurate A4.521 <120, 34> <240, 189> 60 240 fair A4.525 <36, 12> <72, 46> 36 144 accurate A4.526 <72, 40> <144, 186> 36 144 fair A4.655 <24, 12> <48, 48> 24 96 accurate A4.656 <120, 34> <240, 189> 30 120 platonic A4.659 <72, 42> <72, 42> 72 360 accurate A4.663 <36, 10> <36, 10> 36 180 accurate A4.667 <24, 12> <48, 48> 24 120 accurate A4.668 <24, 12> <24, 12> 24 120 accurate A4.670 <120, 34> <120, 34> 120 600 accurate A4.671 <72, 40> <72, 40> 72 360 accurate A4.673 <40, 8> <40, 8> 40 200 accurate A4.678 <60, 5> <120, 34> 60 300 accurate A4.682 <36, 12> <36, 12> 36 180 accurate A4.683 <36, 10> <72, 40> 36 180 accurate A4.720 <36, 10> <72, 46> 36 180 accurate A4.721 <36, 10> <72, 40> 36 180 accurate A4.725 <36, 10> <72, 46> 36 180 accurate A4.806 <12, 3> <24, 12> 24 120 perfect A4.810 <120, 34> <240, 189> 24 120 platonic A4.812 <24, 12> <24, 12> 24 120 accurate A4.813 <12, 4> <24, 14> 24 120 perfect A4.814 <12, 4> <24, 14> 24 120 perfect A4.816 <12, 4> <24, 14> 24 120 perfect A4.820 <24, 12> <48, 48> 24 120 accurate A4.828 <24, 12> <48, 48> 24 120 accurate A4.830 <10, 1> <20, 3> 20 100 perfect A4.831 <10, 2> <20, 2> 20 100 perfect A4.838 <36, 11> <72, 44> 36 216 accurate A4.874 <36, 10> <36, 10> 36 216 accurate A4.875 <36, 10> <36, 10> 36 216 accurate A4.879 <18, 3> <36, 12> 36 216 perfect A4.880 <18, 3> <36, 12> 36 216 perfect A4.886 <18, 3> <18, 3> 18 108 accurate A4.890 <36, 9> <72, 45> 36 216 accurate A4.918 <36, 10> <36, 10> 36 216 accurate A4.930 <24, 12> <24, 12> 24 144 accurate A4.931 <24, 12> <48, 48> 24 144 accurate A4.933 <24, 12> <24, 12> 24 144 accurate A4.934 <24, 12> <24, 12> 24 144 accurate A4.935 <24, 12> <24, 12> 24 144 accurate A4.939 <20, 4> <20, 4> 20 120 accurate A4.947 <10, 2> <20, 5> 20 120 perfect A4.951 <20, 3> <40, 12> 20 120 accurate A4.953 <20, 3> <40, 12> 20 120 accurate A4.961 <18, 3> <18, 3> 18 108 accurate A4.964 <18, 3> <36, 12> 18 108 accurate A4.965 <9, 2> <18, 3> 18 108 perfect A4.1111 <18, 3> <36, 10> 18 108 accurate A4.1211 <18, 4> <36, 9> 36 252 perfect A4.1212 <36, 10> <36, 10> 36 252 accurate A4.1221 <36, 10> <36, 10> 36 252 accurate A4.1242 <24, 12> <24, 12> 24 168 accurate A4.1244 <24, 12> <24, 12> 24 168 accurate A4.1246 <24, 12> <24, 12> 24 168 accurate A4.1248 <10, 2> <20, 2> 20 140 perfect A4.1249 <10, 1> <20, 3> 20 140 perfect A4.1250 <10, 2> <20, 2> 20 140 perfect A4.1251 <10, 1> <20, 3> 20 140 perfect A4.1254 <20, 4> <20, 4> 20 140 accurate A4.1267 <18, 4> <36, 10> 18 126 accurate A4.1277 <9, 2> <18, 3> 18 126 perfect A4.1282 <18, 3> <36, 12> 18 126 accurate A4.1292 <18, 3> <18, 3> 18 126 accurate A4.1489 <18, 3> <18, 3> 18 126 accurate A4.1493 <9, 2> <18, 3> 18 144 perfect A4.1494 <18, 3> <36, 12> 18 144 accurate A4.1495 <18, 4> <36, 10> 18 144 accurate A4.1496 <18, 3> <36, 12> 18 144 accurate A4.1497 <18, 3> <18, 3> 18 144 accurate A4.1504 <9, 2> <18, 3> 18 144 perfect A4.1506 <18, 3> <18, 3> 18 144 accurate A4.1510 <18, 3> <18, 3> 18 144 accurate A4.1868 <12, 4> <12, 4> 12 96 accurate A4.1872 <12, 3> <24, 12> 12 96 accurate A4.1874 <24, 12> <48, 48> 12 96 fair A4.1875 <12, 4> <12, 4> 12 108 accurate A4.1876 <12, 4> <12, 4> 12 108 accurate A4.1883 <12, 3> <12, 3> 12 108 accurate --------------------------------------------------------------------- # perfect maps: 35 # accurate maps: 71 # fair maps: 3 # platonic maps: 2