Polytope of Type {12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12}*24
Also Known As : dodecagon, {12}. if this polytope has another name.
Group : SmallGroup(24,6)
Rank : 2
Schlafli Type : {12}
Number of vertices, edges, etc : 12, 12
Order of s0s1 : 12
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,2} of size 48
   {12,4} of size 96
   {12,4} of size 96
   {12,4} of size 96
   {12,3} of size 96
   {12,6} of size 144
   {12,6} of size 144
   {12,6} of size 144
   {12,3} of size 144
   {12,6} of size 144
   {12,4} of size 192
   {12,8} of size 192
   {12,8} of size 192
   {12,4} of size 192
   {12,4} of size 192
   {12,6} of size 192
   {12,6} of size 192
   {12,4} of size 216
   {12,6} of size 216
   {12,6} of size 216
   {12,6} of size 216
   {12,10} of size 240
   {12,12} of size 288
   {12,12} of size 288
   {12,12} of size 288
   {12,3} of size 288
   {12,4} of size 288
   {12,6} of size 288
   {12,6} of size 288
   {12,14} of size 336
   {12,8} of size 384
   {12,4} of size 384
   {12,8} of size 384
   {12,16} of size 384
   {12,16} of size 384
   {12,4} of size 384
   {12,4} of size 384
   {12,3} of size 384
   {12,8} of size 384
   {12,8} of size 384
   {12,4} of size 384
   {12,12} of size 384
   {12,8} of size 384
   {12,12} of size 384
   {12,8} of size 384
   {12,6} of size 384
   {12,8} of size 384
   {12,8} of size 384
   {12,12} of size 384
   {12,12} of size 384
   {12,4} of size 384
   {12,18} of size 432
   {12,6} of size 432
   {12,6} of size 432
   {12,18} of size 432
   {12,6} of size 432
   {12,9} of size 432
   {12,18} of size 432
   {12,3} of size 432
   {12,6} of size 432
   {12,4} of size 432
   {12,6} of size 432
   {12,6} of size 432
   {12,6} of size 432
   {12,4} of size 432
   {12,6} of size 432
   {12,6} of size 432
   {12,20} of size 480
   {12,4} of size 480
   {12,4} of size 480
   {12,6} of size 480
   {12,6} of size 480
   {12,10} of size 480
   {12,10} of size 480
   {12,10} of size 480
   {12,10} of size 480
   {12,5} of size 480
   {12,15} of size 480
   {12,22} of size 528
   {12,24} of size 576
   {12,12} of size 576
   {12,12} of size 576
   {12,12} of size 576
   {12,24} of size 576
   {12,24} of size 576
   {12,24} of size 576
   {12,24} of size 576
   {12,24} of size 576
   {12,4} of size 576
   {12,8} of size 576
   {12,8} of size 576
   {12,12} of size 576
   {12,12} of size 576
   {12,12} of size 576
   {12,12} of size 576
   {12,6} of size 576
   {12,6} of size 576
   {12,12} of size 576
   {12,12} of size 576
   {12,6} of size 576
   {12,6} of size 576
   {12,6} of size 576
   {12,6} of size 576
   {12,12} of size 576
   {12,12} of size 576
   {12,3} of size 576
   {12,12} of size 576
   {12,10} of size 600
   {12,26} of size 624
   {12,6} of size 648
   {12,12} of size 648
   {12,3} of size 648
   {12,9} of size 648
   {12,9} of size 648
   {12,28} of size 672
   {12,21} of size 672
   {12,30} of size 720
   {12,30} of size 720
   {12,30} of size 720
   {12,6} of size 720
   {12,6} of size 720
   {12,10} of size 720
   {12,15} of size 720
   {12,30} of size 720
   {12,8} of size 768
   {12,16} of size 768
   {12,16} of size 768
   {12,32} of size 768
   {12,32} of size 768
   {12,4} of size 768
   {12,8} of size 768
   {12,8} of size 768
   {12,8} of size 768
   {12,8} of size 768
   {12,8} of size 768
   {12,8} of size 768
   {12,8} of size 768
   {12,6} of size 768
   {12,6} of size 768
   {12,8} of size 768
   {12,8} of size 768
   {12,6} of size 768
   {12,8} of size 768
   {12,6} of size 768
   {12,6} of size 768
   {12,8} of size 768
   {12,8} of size 768
   {12,8} of size 768
   {12,8} of size 768
   {12,24} of size 768
   {12,8} of size 768
   {12,24} of size 768
   {12,4} of size 768
   {12,4} of size 768
   {12,6} of size 768
   {12,8} of size 768
   {12,8} of size 768
   {12,8} of size 768
   {12,12} of size 768
   {12,4} of size 768
   {12,12} of size 768
   {12,8} of size 768
   {12,12} of size 768
   {12,8} of size 768
   {12,24} of size 768
   {12,4} of size 768
   {12,24} of size 768
   {12,6} of size 768
   {12,8} of size 768
   {12,8} of size 768
   {12,24} of size 768
   {12,4} of size 768
   {12,24} of size 768
   {12,6} of size 768
   {12,8} of size 768
   {12,6} of size 768
   {12,4} of size 768
   {12,6} of size 768
   {12,4} of size 768
   {12,34} of size 816
   {12,36} of size 864
   {12,36} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,9} of size 864
   {12,3} of size 864
   {12,4} of size 864
   {12,4} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,18} of size 864
   {12,18} of size 864
   {12,6} of size 864
   {12,6} of size 864
   {12,4} of size 864
   {12,4} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,6} of size 864
   {12,38} of size 912
   {12,20} of size 960
   {12,40} of size 960
   {12,40} of size 960
   {12,10} of size 960
   {12,4} of size 960
   {12,6} of size 960
   {12,4} of size 960
   {12,6} of size 960
   {12,10} of size 960
   {12,10} of size 960
   {12,10} of size 960
   {12,20} of size 960
   {12,30} of size 960
   {12,20} of size 960
   {12,30} of size 960
   {12,10} of size 960
   {12,42} of size 1008
   {12,42} of size 1008
   {12,42} of size 1008
   {12,8} of size 1008
   {12,21} of size 1008
   {12,42} of size 1008
   {12,44} of size 1056
   {12,33} of size 1056
   {12,46} of size 1104
   {12,24} of size 1152
   {12,24} of size 1152
   {12,24} of size 1152
   {12,8} of size 1152
   {12,48} of size 1152
   {12,48} of size 1152
   {12,48} of size 1152
   {12,16} of size 1152
   {12,48} of size 1152
   {12,48} of size 1152
   {12,48} of size 1152
   {12,16} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {12,24} of size 1152
   {12,24} of size 1152
   {12,12} of size 1152
   {12,24} of size 1152
   {12,4} of size 1152
   {12,8} of size 1152
   {12,3} of size 1152
   {12,24} of size 1152
   {12,24} of size 1152
   {12,24} of size 1152
   {12,24} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {12,24} of size 1152
   {12,24} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {12,24} of size 1152
   {12,6} of size 1152
   {12,24} of size 1152
   {12,6} of size 1152
   {12,6} of size 1152
   {12,24} of size 1152
   {12,24} of size 1152
   {12,24} of size 1152
   {12,24} of size 1152
   {12,6} of size 1152
   {12,24} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {12,24} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {12,6} of size 1152
   {12,24} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {12,24} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {12,24} of size 1152
   {12,6} of size 1152
   {12,24} of size 1152
   {12,3} of size 1152
   {12,6} of size 1152
   {12,24} of size 1152
   {12,24} of size 1152
   {12,6} of size 1152
   {12,6} of size 1152
   {12,4} of size 1152
   {12,8} of size 1152
   {12,6} of size 1152
   {12,12} of size 1152
   {12,14} of size 1176
   {12,50} of size 1200
   {12,6} of size 1200
   {12,10} of size 1200
   {12,10} of size 1200
   {12,6} of size 1200
   {12,4} of size 1200
   {12,10} of size 1200
   {12,52} of size 1248
   {12,39} of size 1248
   {12,18} of size 1296
   {12,54} of size 1296
   {12,6} of size 1296
   {12,6} of size 1296
   {12,18} of size 1296
   {12,18} of size 1296
   {12,18} of size 1296
   {12,6} of size 1296
   {12,18} of size 1296
   {12,54} of size 1296
   {12,18} of size 1296
   {12,18} of size 1296
   {12,18} of size 1296
   {12,6} of size 1296
   {12,27} of size 1296
   {12,54} of size 1296
   {12,3} of size 1296
   {12,18} of size 1296
   {12,9} of size 1296
   {12,18} of size 1296
   {12,6} of size 1296
   {12,9} of size 1296
   {12,9} of size 1296
   {12,18} of size 1296
   {12,6} of size 1296
   {12,9} of size 1296
   {12,18} of size 1296
   {12,6} of size 1296
   {12,6} of size 1296
   {12,6} of size 1296
   {12,4} of size 1296
   {12,6} of size 1296
   {12,6} of size 1296
   {12,6} of size 1296
   {12,6} of size 1296
   {12,6} of size 1296
   {12,12} of size 1296
   {12,12} of size 1296
   {12,12} of size 1296
   {12,12} of size 1296
   {12,6} of size 1296
   {12,12} of size 1296
   {12,6} of size 1296
   {12,3} of size 1296
   {12,6} of size 1296
   {12,6} of size 1296
   {12,9} of size 1296
   {12,9} of size 1296
   {12,18} of size 1296
   {12,18} of size 1296
   {12,18} of size 1296
   {12,18} of size 1296
   {12,6} of size 1296
   {12,12} of size 1296
   {12,6} of size 1296
   {12,6} of size 1296
   {12,12} of size 1296
   {12,12} of size 1296
   {12,3} of size 1320
   {12,3} of size 1320
   {12,4} of size 1320
   {12,4} of size 1320
   {12,5} of size 1320
   {12,5} of size 1320
   {12,5} of size 1320
   {12,5} of size 1320
   {12,6} of size 1320
   {12,6} of size 1320
   {12,10} of size 1320
   {12,10} of size 1320
   {12,10} of size 1320
   {12,10} of size 1320
   {12,11} of size 1320
   {12,11} of size 1320
   {12,12} of size 1320
   {12,12} of size 1320
   {12,28} of size 1344
   {12,56} of size 1344
   {12,56} of size 1344
   {12,8} of size 1344
   {12,8} of size 1344
   {12,7} of size 1344
   {12,4} of size 1344
   {12,4} of size 1344
   {12,6} of size 1344
   {12,6} of size 1344
   {12,8} of size 1344
   {12,8} of size 1344
   {12,8} of size 1344
   {12,8} of size 1344
   {12,8} of size 1344
   {12,8} of size 1344
   {12,28} of size 1344
   {12,42} of size 1344
   {12,28} of size 1344
   {12,42} of size 1344
   {12,58} of size 1392
   {12,60} of size 1440
   {12,60} of size 1440
   {12,60} of size 1440
   {12,6} of size 1440
   {12,6} of size 1440
   {12,10} of size 1440
   {12,10} of size 1440
   {12,10} of size 1440
   {12,10} of size 1440
   {12,12} of size 1440
   {12,12} of size 1440
   {12,12} of size 1440
   {12,12} of size 1440
   {12,10} of size 1440
   {12,10} of size 1440
   {12,15} of size 1440
   {12,15} of size 1440
   {12,15} of size 1440
   {12,20} of size 1440
   {12,15} of size 1440
   {12,6} of size 1440
   {12,6} of size 1440
   {12,10} of size 1440
   {12,30} of size 1440
   {12,30} of size 1440
   {12,62} of size 1488
   {12,66} of size 1584
   {12,66} of size 1584
   {12,66} of size 1584
   {12,33} of size 1584
   {12,66} of size 1584
   {12,68} of size 1632
   {12,51} of size 1632
   {12,70} of size 1680
   {12,24} of size 1728
   {12,36} of size 1728
   {12,36} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,24} of size 1728
   {12,72} of size 1728
   {12,72} of size 1728
   {12,24} of size 1728
   {12,24} of size 1728
   {12,72} of size 1728
   {12,72} of size 1728
   {12,24} of size 1728
   {12,24} of size 1728
   {12,4} of size 1728
   {12,4} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,8} of size 1728
   {12,24} of size 1728
   {12,24} of size 1728
   {12,8} of size 1728
   {12,24} of size 1728
   {12,24} of size 1728
   {12,8} of size 1728
   {12,24} of size 1728
   {12,24} of size 1728
   {12,8} of size 1728
   {12,24} of size 1728
   {12,24} of size 1728
   {12,24} of size 1728
   {12,24} of size 1728
   {12,12} of size 1728
   {12,36} of size 1728
   {12,18} of size 1728
   {12,18} of size 1728
   {12,36} of size 1728
   {12,36} of size 1728
   {12,36} of size 1728
   {12,18} of size 1728
   {12,36} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,6} of size 1728
   {12,6} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,6} of size 1728
   {12,6} of size 1728
   {12,18} of size 1728
   {12,36} of size 1728
   {12,6} of size 1728
   {12,6} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,8} of size 1728
   {12,24} of size 1728
   {12,8} of size 1728
   {12,24} of size 1728
   {12,8} of size 1728
   {12,24} of size 1728
   {12,8} of size 1728
   {12,24} of size 1728
   {12,4} of size 1728
   {12,4} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,24} of size 1728
   {12,24} of size 1728
   {12,24} of size 1728
   {12,24} of size 1728
   {12,9} of size 1728
   {12,36} of size 1728
   {12,3} of size 1728
   {12,12} of size 1728
   {12,6} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,6} of size 1728
   {12,6} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,4} of size 1728
   {12,6} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,74} of size 1776
   {12,76} of size 1824
   {12,57} of size 1824
   {12,78} of size 1872
   {12,78} of size 1872
   {12,78} of size 1872
   {12,39} of size 1872
   {12,78} of size 1872
   {12,40} of size 1920
   {12,80} of size 1920
   {12,80} of size 1920
   {12,40} of size 1920
   {12,20} of size 1920
   {12,15} of size 1920
   {12,40} of size 1920
   {12,40} of size 1920
   {12,40} of size 1920
   {12,40} of size 1920
   {12,60} of size 1920
   {12,60} of size 1920
   {12,20} of size 1920
   {12,20} of size 1920
   {12,60} of size 1920
   {12,30} of size 1920
   {12,40} of size 1920
   {12,40} of size 1920
   {12,60} of size 1920
   {12,20} of size 1920
   {12,20} of size 1920
   {12,10} of size 1920
   {12,4} of size 1920
   {12,20} of size 1920
   {12,12} of size 1920
   {12,20} of size 1920
   {12,8} of size 1920
   {12,10} of size 1920
   {12,6} of size 1920
   {12,8} of size 1920
   {12,12} of size 1920
   {12,20} of size 1920
   {12,12} of size 1920
   {12,12} of size 1920
   {12,8} of size 1920
   {12,20} of size 1920
   {12,20} of size 1920
   {12,8} of size 1920
   {12,4} of size 1920
   {12,10} of size 1920
   {12,20} of size 1920
   {12,20} of size 1920
   {12,20} of size 1920
   {12,4} of size 1920
   {12,5} of size 1920
   {12,5} of size 1920
   {12,6} of size 1920
   {12,8} of size 1920
   {12,12} of size 1920
   {12,5} of size 1920
   {12,5} of size 1920
   {12,5} of size 1920
   {12,5} of size 1920
   {12,4} of size 1944
   {12,18} of size 1944
   {12,18} of size 1944
   {12,4} of size 1944
   {12,4} of size 1944
   {12,6} of size 1944
   {12,6} of size 1944
   {12,12} of size 1944
   {12,12} of size 1944
   {12,18} of size 1944
   {12,18} of size 1944
   {12,4} of size 1944
   {12,12} of size 1944
   {12,18} of size 1944
   {12,18} of size 1944
   {12,18} of size 1944
   {12,6} of size 1944
   {12,12} of size 1944
   {12,12} of size 1944
   {12,12} of size 1944
   {12,18} of size 1944
   {12,18} of size 1944
   {12,9} of size 1944
   {12,9} of size 1944
   {12,9} of size 1944
   {12,82} of size 1968
Vertex Figure Of :
   {2,12} of size 48
   {4,12} of size 96
   {4,12} of size 96
   {4,12} of size 96
   {3,12} of size 96
   {6,12} of size 144
   {6,12} of size 144
   {6,12} of size 144
   {3,12} of size 144
   {6,12} of size 144
   {4,12} of size 192
   {8,12} of size 192
   {8,12} of size 192
   {4,12} of size 192
   {4,12} of size 192
   {6,12} of size 192
   {6,12} of size 192
   {4,12} of size 216
   {6,12} of size 216
   {6,12} of size 216
   {6,12} of size 216
   {10,12} of size 240
   {12,12} of size 288
   {12,12} of size 288
   {12,12} of size 288
   {3,12} of size 288
   {4,12} of size 288
   {6,12} of size 288
   {6,12} of size 288
   {14,12} of size 336
   {8,12} of size 384
   {4,12} of size 384
   {8,12} of size 384
   {16,12} of size 384
   {16,12} of size 384
   {4,12} of size 384
   {4,12} of size 384
   {3,12} of size 384
   {8,12} of size 384
   {8,12} of size 384
   {4,12} of size 384
   {12,12} of size 384
   {8,12} of size 384
   {12,12} of size 384
   {8,12} of size 384
   {6,12} of size 384
   {8,12} of size 384
   {8,12} of size 384
   {12,12} of size 384
   {12,12} of size 384
   {4,12} of size 384
   {18,12} of size 432
   {6,12} of size 432
   {6,12} of size 432
   {18,12} of size 432
   {6,12} of size 432
   {9,12} of size 432
   {18,12} of size 432
   {3,12} of size 432
   {6,12} of size 432
   {4,12} of size 432
   {6,12} of size 432
   {6,12} of size 432
   {6,12} of size 432
   {4,12} of size 432
   {6,12} of size 432
   {6,12} of size 432
   {20,12} of size 480
   {4,12} of size 480
   {4,12} of size 480
   {6,12} of size 480
   {6,12} of size 480
   {10,12} of size 480
   {10,12} of size 480
   {10,12} of size 480
   {10,12} of size 480
   {5,12} of size 480
   {15,12} of size 480
   {22,12} of size 528
   {24,12} of size 576
   {12,12} of size 576
   {12,12} of size 576
   {12,12} of size 576
   {24,12} of size 576
   {24,12} of size 576
   {24,12} of size 576
   {24,12} of size 576
   {24,12} of size 576
   {4,12} of size 576
   {8,12} of size 576
   {8,12} of size 576
   {12,12} of size 576
   {12,12} of size 576
   {12,12} of size 576
   {12,12} of size 576
   {6,12} of size 576
   {6,12} of size 576
   {12,12} of size 576
   {12,12} of size 576
   {6,12} of size 576
   {6,12} of size 576
   {6,12} of size 576
   {6,12} of size 576
   {12,12} of size 576
   {12,12} of size 576
   {3,12} of size 576
   {12,12} of size 576
   {10,12} of size 600
   {26,12} of size 624
   {6,12} of size 648
   {12,12} of size 648
   {3,12} of size 648
   {9,12} of size 648
   {9,12} of size 648
   {28,12} of size 672
   {21,12} of size 672
   {30,12} of size 720
   {30,12} of size 720
   {30,12} of size 720
   {6,12} of size 720
   {6,12} of size 720
   {10,12} of size 720
   {15,12} of size 720
   {30,12} of size 720
   {8,12} of size 768
   {16,12} of size 768
   {16,12} of size 768
   {32,12} of size 768
   {32,12} of size 768
   {4,12} of size 768
   {8,12} of size 768
   {8,12} of size 768
   {8,12} of size 768
   {8,12} of size 768
   {8,12} of size 768
   {8,12} of size 768
   {8,12} of size 768
   {6,12} of size 768
   {6,12} of size 768
   {8,12} of size 768
   {8,12} of size 768
   {6,12} of size 768
   {8,12} of size 768
   {6,12} of size 768
   {6,12} of size 768
   {8,12} of size 768
   {8,12} of size 768
   {8,12} of size 768
   {8,12} of size 768
   {24,12} of size 768
   {8,12} of size 768
   {24,12} of size 768
   {4,12} of size 768
   {4,12} of size 768
   {6,12} of size 768
   {8,12} of size 768
   {8,12} of size 768
   {8,12} of size 768
   {12,12} of size 768
   {4,12} of size 768
   {12,12} of size 768
   {8,12} of size 768
   {12,12} of size 768
   {8,12} of size 768
   {24,12} of size 768
   {4,12} of size 768
   {24,12} of size 768
   {6,12} of size 768
   {8,12} of size 768
   {8,12} of size 768
   {24,12} of size 768
   {4,12} of size 768
   {24,12} of size 768
   {6,12} of size 768
   {8,12} of size 768
   {6,12} of size 768
   {4,12} of size 768
   {6,12} of size 768
   {4,12} of size 768
   {34,12} of size 816
   {36,12} of size 864
   {36,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {9,12} of size 864
   {3,12} of size 864
   {4,12} of size 864
   {4,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {18,12} of size 864
   {18,12} of size 864
   {6,12} of size 864
   {6,12} of size 864
   {4,12} of size 864
   {4,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {12,12} of size 864
   {6,12} of size 864
   {38,12} of size 912
   {20,12} of size 960
   {40,12} of size 960
   {40,12} of size 960
   {10,12} of size 960
   {4,12} of size 960
   {6,12} of size 960
   {4,12} of size 960
   {6,12} of size 960
   {10,12} of size 960
   {10,12} of size 960
   {10,12} of size 960
   {20,12} of size 960
   {30,12} of size 960
   {20,12} of size 960
   {30,12} of size 960
   {10,12} of size 960
   {42,12} of size 1008
   {42,12} of size 1008
   {42,12} of size 1008
   {8,12} of size 1008
   {21,12} of size 1008
   {42,12} of size 1008
   {44,12} of size 1056
   {33,12} of size 1056
   {46,12} of size 1104
   {24,12} of size 1152
   {24,12} of size 1152
   {24,12} of size 1152
   {8,12} of size 1152
   {48,12} of size 1152
   {48,12} of size 1152
   {48,12} of size 1152
   {16,12} of size 1152
   {48,12} of size 1152
   {48,12} of size 1152
   {48,12} of size 1152
   {16,12} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {24,12} of size 1152
   {24,12} of size 1152
   {12,12} of size 1152
   {24,12} of size 1152
   {4,12} of size 1152
   {8,12} of size 1152
   {3,12} of size 1152
   {24,12} of size 1152
   {24,12} of size 1152
   {24,12} of size 1152
   {24,12} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {24,12} of size 1152
   {24,12} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {24,12} of size 1152
   {6,12} of size 1152
   {24,12} of size 1152
   {6,12} of size 1152
   {6,12} of size 1152
   {24,12} of size 1152
   {24,12} of size 1152
   {24,12} of size 1152
   {24,12} of size 1152
   {6,12} of size 1152
   {24,12} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {24,12} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {6,12} of size 1152
   {24,12} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {24,12} of size 1152
   {12,12} of size 1152
   {12,12} of size 1152
   {24,12} of size 1152
   {6,12} of size 1152
   {24,12} of size 1152
   {3,12} of size 1152
   {6,12} of size 1152
   {24,12} of size 1152
   {24,12} of size 1152
   {6,12} of size 1152
   {6,12} of size 1152
   {4,12} of size 1152
   {8,12} of size 1152
   {6,12} of size 1152
   {12,12} of size 1152
   {14,12} of size 1176
   {50,12} of size 1200
   {6,12} of size 1200
   {10,12} of size 1200
   {10,12} of size 1200
   {6,12} of size 1200
   {4,12} of size 1200
   {10,12} of size 1200
   {52,12} of size 1248
   {39,12} of size 1248
   {18,12} of size 1296
   {54,12} of size 1296
   {6,12} of size 1296
   {6,12} of size 1296
   {18,12} of size 1296
   {18,12} of size 1296
   {18,12} of size 1296
   {6,12} of size 1296
   {18,12} of size 1296
   {54,12} of size 1296
   {18,12} of size 1296
   {18,12} of size 1296
   {18,12} of size 1296
   {6,12} of size 1296
   {27,12} of size 1296
   {54,12} of size 1296
   {3,12} of size 1296
   {18,12} of size 1296
   {9,12} of size 1296
   {18,12} of size 1296
   {6,12} of size 1296
   {9,12} of size 1296
   {9,12} of size 1296
   {18,12} of size 1296
   {6,12} of size 1296
   {9,12} of size 1296
   {18,12} of size 1296
   {6,12} of size 1296
   {6,12} of size 1296
   {6,12} of size 1296
   {4,12} of size 1296
   {6,12} of size 1296
   {6,12} of size 1296
   {6,12} of size 1296
   {6,12} of size 1296
   {6,12} of size 1296
   {12,12} of size 1296
   {12,12} of size 1296
   {12,12} of size 1296
   {12,12} of size 1296
   {6,12} of size 1296
   {12,12} of size 1296
   {6,12} of size 1296
   {3,12} of size 1296
   {6,12} of size 1296
   {6,12} of size 1296
   {9,12} of size 1296
   {9,12} of size 1296
   {18,12} of size 1296
   {18,12} of size 1296
   {18,12} of size 1296
   {18,12} of size 1296
   {6,12} of size 1296
   {12,12} of size 1296
   {6,12} of size 1296
   {6,12} of size 1296
   {12,12} of size 1296
   {12,12} of size 1296
   {3,12} of size 1320
   {3,12} of size 1320
   {4,12} of size 1320
   {4,12} of size 1320
   {5,12} of size 1320
   {5,12} of size 1320
   {5,12} of size 1320
   {5,12} of size 1320
   {6,12} of size 1320
   {6,12} of size 1320
   {10,12} of size 1320
   {10,12} of size 1320
   {10,12} of size 1320
   {10,12} of size 1320
   {11,12} of size 1320
   {11,12} of size 1320
   {12,12} of size 1320
   {12,12} of size 1320
   {28,12} of size 1344
   {56,12} of size 1344
   {56,12} of size 1344
   {8,12} of size 1344
   {8,12} of size 1344
   {7,12} of size 1344
   {4,12} of size 1344
   {4,12} of size 1344
   {6,12} of size 1344
   {6,12} of size 1344
   {8,12} of size 1344
   {8,12} of size 1344
   {8,12} of size 1344
   {8,12} of size 1344
   {8,12} of size 1344
   {8,12} of size 1344
   {28,12} of size 1344
   {42,12} of size 1344
   {28,12} of size 1344
   {42,12} of size 1344
   {58,12} of size 1392
   {60,12} of size 1440
   {60,12} of size 1440
   {60,12} of size 1440
   {6,12} of size 1440
   {6,12} of size 1440
   {10,12} of size 1440
   {10,12} of size 1440
   {10,12} of size 1440
   {10,12} of size 1440
   {12,12} of size 1440
   {12,12} of size 1440
   {12,12} of size 1440
   {12,12} of size 1440
   {10,12} of size 1440
   {10,12} of size 1440
   {15,12} of size 1440
   {15,12} of size 1440
   {15,12} of size 1440
   {20,12} of size 1440
   {15,12} of size 1440
   {6,12} of size 1440
   {6,12} of size 1440
   {10,12} of size 1440
   {30,12} of size 1440
   {30,12} of size 1440
   {62,12} of size 1488
   {66,12} of size 1584
   {66,12} of size 1584
   {66,12} of size 1584
   {33,12} of size 1584
   {66,12} of size 1584
   {68,12} of size 1632
   {51,12} of size 1632
   {70,12} of size 1680
   {24,12} of size 1728
   {36,12} of size 1728
   {36,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {24,12} of size 1728
   {72,12} of size 1728
   {72,12} of size 1728
   {24,12} of size 1728
   {24,12} of size 1728
   {72,12} of size 1728
   {72,12} of size 1728
   {24,12} of size 1728
   {24,12} of size 1728
   {4,12} of size 1728
   {4,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {8,12} of size 1728
   {24,12} of size 1728
   {24,12} of size 1728
   {8,12} of size 1728
   {24,12} of size 1728
   {24,12} of size 1728
   {8,12} of size 1728
   {24,12} of size 1728
   {24,12} of size 1728
   {8,12} of size 1728
   {24,12} of size 1728
   {24,12} of size 1728
   {24,12} of size 1728
   {24,12} of size 1728
   {12,12} of size 1728
   {36,12} of size 1728
   {18,12} of size 1728
   {18,12} of size 1728
   {36,12} of size 1728
   {36,12} of size 1728
   {36,12} of size 1728
   {18,12} of size 1728
   {36,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {6,12} of size 1728
   {6,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {6,12} of size 1728
   {6,12} of size 1728
   {18,12} of size 1728
   {36,12} of size 1728
   {6,12} of size 1728
   {6,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {8,12} of size 1728
   {24,12} of size 1728
   {8,12} of size 1728
   {24,12} of size 1728
   {8,12} of size 1728
   {24,12} of size 1728
   {8,12} of size 1728
   {24,12} of size 1728
   {4,12} of size 1728
   {4,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {24,12} of size 1728
   {24,12} of size 1728
   {24,12} of size 1728
   {24,12} of size 1728
   {9,12} of size 1728
   {36,12} of size 1728
   {3,12} of size 1728
   {12,12} of size 1728
   {6,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {6,12} of size 1728
   {6,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {4,12} of size 1728
   {6,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {12,12} of size 1728
   {74,12} of size 1776
   {76,12} of size 1824
   {57,12} of size 1824
   {78,12} of size 1872
   {78,12} of size 1872
   {78,12} of size 1872
   {39,12} of size 1872
   {78,12} of size 1872
   {40,12} of size 1920
   {80,12} of size 1920
   {80,12} of size 1920
   {40,12} of size 1920
   {20,12} of size 1920
   {15,12} of size 1920
   {40,12} of size 1920
   {40,12} of size 1920
   {40,12} of size 1920
   {40,12} of size 1920
   {60,12} of size 1920
   {60,12} of size 1920
   {20,12} of size 1920
   {20,12} of size 1920
   {60,12} of size 1920
   {30,12} of size 1920
   {40,12} of size 1920
   {40,12} of size 1920
   {60,12} of size 1920
   {20,12} of size 1920
   {20,12} of size 1920
   {10,12} of size 1920
   {4,12} of size 1920
   {20,12} of size 1920
   {12,12} of size 1920
   {20,12} of size 1920
   {8,12} of size 1920
   {10,12} of size 1920
   {6,12} of size 1920
   {8,12} of size 1920
   {12,12} of size 1920
   {20,12} of size 1920
   {12,12} of size 1920
   {12,12} of size 1920
   {8,12} of size 1920
   {20,12} of size 1920
   {20,12} of size 1920
   {8,12} of size 1920
   {4,12} of size 1920
   {10,12} of size 1920
   {20,12} of size 1920
   {20,12} of size 1920
   {20,12} of size 1920
   {4,12} of size 1920
   {5,12} of size 1920
   {5,12} of size 1920
   {6,12} of size 1920
   {8,12} of size 1920
   {12,12} of size 1920
   {5,12} of size 1920
   {5,12} of size 1920
   {5,12} of size 1920
   {5,12} of size 1920
   {4,12} of size 1944
   {18,12} of size 1944
   {18,12} of size 1944
   {4,12} of size 1944
   {4,12} of size 1944
   {6,12} of size 1944
   {6,12} of size 1944
   {12,12} of size 1944
   {12,12} of size 1944
   {18,12} of size 1944
   {18,12} of size 1944
   {4,12} of size 1944
   {12,12} of size 1944
   {18,12} of size 1944
   {18,12} of size 1944
   {18,12} of size 1944
   {6,12} of size 1944
   {12,12} of size 1944
   {12,12} of size 1944
   {12,12} of size 1944
   {18,12} of size 1944
   {18,12} of size 1944
   {9,12} of size 1944
   {9,12} of size 1944
   {9,12} of size 1944
   {82,12} of size 1968
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6}*12
   3-fold quotients : {4}*8
   4-fold quotients : {3}*6
   6-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24}*48
   3-fold covers : {36}*72
   4-fold covers : {48}*96
   5-fold covers : {60}*120
   6-fold covers : {72}*144
   7-fold covers : {84}*168
   8-fold covers : {96}*192
   9-fold covers : {108}*216
   10-fold covers : {120}*240
   11-fold covers : {132}*264
   12-fold covers : {144}*288
   13-fold covers : {156}*312
   14-fold covers : {168}*336
   15-fold covers : {180}*360
   16-fold covers : {192}*384
   17-fold covers : {204}*408
   18-fold covers : {216}*432
   19-fold covers : {228}*456
   20-fold covers : {240}*480
   21-fold covers : {252}*504
   22-fold covers : {264}*528
   23-fold covers : {276}*552
   24-fold covers : {288}*576
   25-fold covers : {300}*600
   26-fold covers : {312}*624
   27-fold covers : {324}*648
   28-fold covers : {336}*672
   29-fold covers : {348}*696
   30-fold covers : {360}*720
   31-fold covers : {372}*744
   32-fold covers : {384}*768
   33-fold covers : {396}*792
   34-fold covers : {408}*816
   35-fold covers : {420}*840
   36-fold covers : {432}*864
   37-fold covers : {444}*888
   38-fold covers : {456}*912
   39-fold covers : {468}*936
   40-fold covers : {480}*960
   41-fold covers : {492}*984
   42-fold covers : {504}*1008
   43-fold covers : {516}*1032
   44-fold covers : {528}*1056
   45-fold covers : {540}*1080
   46-fold covers : {552}*1104
   47-fold covers : {564}*1128
   48-fold covers : {576}*1152
   49-fold covers : {588}*1176
   50-fold covers : {600}*1200
   51-fold covers : {612}*1224
   52-fold covers : {624}*1248
   53-fold covers : {636}*1272
   54-fold covers : {648}*1296
   55-fold covers : {660}*1320
   56-fold covers : {672}*1344
   57-fold covers : {684}*1368
   58-fold covers : {696}*1392
   59-fold covers : {708}*1416
   60-fold covers : {720}*1440
   61-fold covers : {732}*1464
   62-fold covers : {744}*1488
   63-fold covers : {756}*1512
   65-fold covers : {780}*1560
   66-fold covers : {792}*1584
   67-fold covers : {804}*1608
   68-fold covers : {816}*1632
   69-fold covers : {828}*1656
   70-fold covers : {840}*1680
   71-fold covers : {852}*1704
   72-fold covers : {864}*1728
   73-fold covers : {876}*1752
   74-fold covers : {888}*1776
   75-fold covers : {900}*1800
   76-fold covers : {912}*1824
   77-fold covers : {924}*1848
   78-fold covers : {936}*1872
   79-fold covers : {948}*1896
   80-fold covers : {960}*1920
   81-fold covers : {972}*1944
   82-fold covers : {984}*1968
   83-fold covers : {996}*1992
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);;
s1 := ( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);;
poly := Group([s0,s1]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(12)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(12)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
poly := sub<Sym(12)|s0,s1>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope