Polytopes for The Mathieu Group M12
The Mathieu Group M12 has :
- 40 rank 3 polytopes,
- 27 rank 4 polytopes,
- 0 rank 5 polytopes,
- and no higher rank polytopes.
Polytopes of rank 4
| index | Type | Facet Group | VF Group | Dual |
|---|
| m12[41] | {5,5,4} | Simple, Order 660 | Order 120 | m12[48] |
| m12[42] | {5,6,4} | Simple, Order 660 | Order 1440 | m12[49] |
| m12[43] | {3,10,4} | Order 720 | Order 1440 | m12[47] |
| m12[44] | {3,8,4} | Order 720 | Order 1440 | m12[46] |
| m12[45] | {3,6,4} | Solvable, Order 108 | Order 1440 | m12[50] |
| m12[46] | {4,8,3} | Order 1440 | Order 720 | m12[44] |
| m12[47] | {4,10,3} | Order 1440 | Order 720 | m12[43] |
| m12[48] | {4,5,5} | Order 120 | Simple, Order 660 | m12[41] |
| m12[49] | {4,6,5} | Order 1440 | Simple, Order 660 | m12[42] |
| m12[50] | {4,6,3} | Order 1440 | Solvable, Order 108 | m12[45] |
| m12[51] | {4,8,4} | Order 1440 | Order 720 | m12[52] |
| m12[52] | {4,8,4} | Order 720 | Order 1440 | m12[51] |
| m12[53] | {4,5,5} | Order 720 | Simple, Order 660 | m12[60] |
| m12[54] | {4,5,3} | Order 720 | Simple, Order 60 | m12[67] |
| m12[55] | {4,6,6} | Order 240 | Simple, Order 660 | m12[64] |
| m12[56] | {4,6,5} | Order 240 | Simple, Order 660 | m12[58] |
| m12[57] | {4,5,6} | Order 240 | Simple, Order 660 | m12[63] |
| m12[58] | {5,6,4} | Simple, Order 660 | Order 240 | m12[56] |
| m12[59] | {5,3,6} | Simple, Order 60 | Solvable, Order 192 | m12[61] |
| m12[60] | {5,5,4} | Simple, Order 660 | Order 720 | m12[53] |
| m12[61] | {6,3,5} | Solvable, Order 192 | Simple, Order 60 | m12[59] |
| m12[62] | {6,3,6} | Solvable, Order 192 | Solvable, Order 192 | m12[62] |
| m12[63] | {6,5,4} | Simple, Order 660 | Order 240 | m12[57] |
| m12[64] | {6,6,4} | Simple, Order 660 | Order 240 | m12[55] |
| m12[65] | {6,6,3} | Simple, Order 660 | Solvable, Order 192 | m12[66] |
| m12[66] | {3,6,6} | Solvable, Order 192 | Simple, Order 660 | m12[65] |
| m12[67] | {3,5,4} | Simple, Order 60 | Order 720 | m12[54] |
Polytopes of rank 3
| index | Type | Dual |
|---|
| 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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