Polytopes for The Mathieu Group M12

The Mathieu Group M12 has :


Polytopes of rank 4

indexTypeFacet GroupVF GroupDual
m12[41]{5,5,4}Simple, Order 660Order 120m12[48]
m12[42]{5,6,4}Simple, Order 660Order 1440m12[49]
m12[43]{3,10,4}Order 720Order 1440m12[47]
m12[44]{3,8,4}Order 720Order 1440m12[46]
m12[45]{3,6,4}Solvable, Order 108Order 1440m12[50]
m12[46]{4,8,3}Order 1440Order 720m12[44]
m12[47]{4,10,3}Order 1440Order 720m12[43]
m12[48]{4,5,5}Order 120Simple, Order 660m12[41]
m12[49]{4,6,5}Order 1440Simple, Order 660m12[42]
m12[50]{4,6,3}Order 1440Solvable, Order 108m12[45]
m12[51]{4,8,4}Order 1440Order 720m12[52]
m12[52]{4,8,4}Order 720Order 1440m12[51]
m12[53]{4,5,5}Order 720Simple, Order 660m12[60]
m12[54]{4,5,3}Order 720Simple, Order 60m12[67]
m12[55]{4,6,6}Order 240Simple, Order 660m12[64]
m12[56]{4,6,5}Order 240Simple, Order 660m12[58]
m12[57]{4,5,6}Order 240Simple, Order 660m12[63]
m12[58]{5,6,4}Simple, Order 660Order 240m12[56]
m12[59]{5,3,6}Simple, Order 60Solvable, Order 192m12[61]
m12[60]{5,5,4}Simple, Order 660Order 720m12[53]
m12[61]{6,3,5}Solvable, Order 192Simple, Order 60m12[59]
m12[62]{6,3,6}Solvable, Order 192Solvable, Order 192m12[62]
m12[63]{6,5,4}Simple, Order 660Order 240m12[57]
m12[64]{6,6,4}Simple, Order 660Order 240m12[55]
m12[65]{6,6,3}Simple, Order 660Solvable, Order 192m12[66]
m12[66]{3,6,6}Solvable, Order 192Simple, Order 660m12[65]
m12[67]{3,5,4}Simple, Order 60Order 720m12[54]

Polytopes of rank 3

indexTypeDual
m12[1]{6,8}m12[23]
m12[2]{6,10}m12[16]
m12[3]{6,8}m12[31]
m12[4]{6,6}m12[34]
m12[5]{10,6}m12[13]
m12[6]{10,8}m12[10]
m12[7]{8,6}m12[15]
m12[8]{8,8}m12[8]
m12[9]{8,8}m12[9]
m12[10]{8,10}m12[6]
m12[11]{8,5}m12[37]
m12[12]{8,6}m12[39]
m12[13]{6,10}m12[5]
m12[14]{6,6}m12[14]
m12[15]{6,8}m12[7]
m12[16]{10,6}m12[2]
m12[17]{10,10}m12[17]
m12[18]{10,8}m12[25]
m12[19]{10,8}m12[22]
m12[20]{10,8}m12[26]
m12[21]{10,8}m12[33]
m12[22]{8,10}m12[19]
m12[23]{8,6}m12[1]
m12[24]{8,8}m12[27]
m12[25]{8,10}m12[18]
m12[26]{8,10}m12[20]
m12[27]{8,8}m12[24]
m12[28]{8,6}m12[35]
m12[29]{8,8}m12[29]
m12[30]{8,8}m12[30]
m12[31]{8,6}m12[3]
m12[32]{8,6}m12[36]
m12[33]{8,10}m12[21]
m12[34]{6,6}m12[4]
m12[35]{6,8}m12[28]
m12[36]{6,8}m12[32]
m12[37]{5,8}m12[11]
m12[38]{5,6}m12[40]
m12[39]{6,8}m12[12]
m12[40]{6,5}m12[38]

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