Polytope of Type {2,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12}*48
if this polytope has a name.
Group : SmallGroup(48,36)
Rank : 3
Schlafli Type : {2,12}
Number of vertices, edges, etc : 2, 12, 12
Order of s0s1s2 : 12
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,12,2} of size 96
{2,12,4} of size 192
{2,12,4} of size 192
{2,12,4} of size 192
{2,12,3} of size 192
{2,12,6} of size 288
{2,12,6} of size 288
{2,12,6} of size 288
{2,12,3} of size 288
{2,12,6} of size 288
{2,12,4} of size 384
{2,12,8} of size 384
{2,12,8} of size 384
{2,12,4} of size 384
{2,12,4} of size 384
{2,12,6} of size 384
{2,12,6} of size 384
{2,12,4} of size 432
{2,12,6} of size 432
{2,12,6} of size 432
{2,12,6} of size 432
{2,12,10} of size 480
{2,12,12} of size 576
{2,12,12} of size 576
{2,12,12} of size 576
{2,12,3} of size 576
{2,12,4} of size 576
{2,12,6} of size 576
{2,12,6} of size 576
{2,12,14} of size 672
{2,12,8} of size 768
{2,12,16} of size 768
{2,12,16} of size 768
{2,12,4} of size 768
{2,12,8} of size 768
{2,12,3} of size 768
{2,12,8} of size 768
{2,12,8} of size 768
{2,12,4} of size 768
{2,12,4} of size 768
{2,12,4} of size 768
{2,12,12} of size 768
{2,12,8} of size 768
{2,12,12} of size 768
{2,12,8} of size 768
{2,12,6} of size 768
{2,12,8} of size 768
{2,12,8} of size 768
{2,12,12} of size 768
{2,12,12} of size 768
{2,12,4} of size 768
{2,12,18} of size 864
{2,12,6} of size 864
{2,12,6} of size 864
{2,12,18} of size 864
{2,12,6} of size 864
{2,12,9} of size 864
{2,12,18} of size 864
{2,12,3} of size 864
{2,12,6} of size 864
{2,12,4} of size 864
{2,12,6} of size 864
{2,12,6} of size 864
{2,12,6} of size 864
{2,12,4} of size 864
{2,12,6} of size 864
{2,12,6} of size 864
{2,12,20} of size 960
{2,12,4} of size 960
{2,12,4} of size 960
{2,12,6} of size 960
{2,12,6} of size 960
{2,12,10} of size 960
{2,12,10} of size 960
{2,12,10} of size 960
{2,12,10} of size 960
{2,12,5} of size 960
{2,12,15} of size 960
{2,12,22} of size 1056
{2,12,24} of size 1152
{2,12,24} of size 1152
{2,12,24} of size 1152
{2,12,8} of size 1152
{2,12,24} of size 1152
{2,12,24} of size 1152
{2,12,24} of size 1152
{2,12,8} of size 1152
{2,12,12} of size 1152
{2,12,12} of size 1152
{2,12,12} of size 1152
{2,12,4} of size 1152
{2,12,12} of size 1152
{2,12,12} of size 1152
{2,12,12} of size 1152
{2,12,12} of size 1152
{2,12,6} of size 1152
{2,12,6} of size 1152
{2,12,12} of size 1152
{2,12,12} of size 1152
{2,12,6} of size 1152
{2,12,6} of size 1152
{2,12,6} of size 1152
{2,12,6} of size 1152
{2,12,12} of size 1152
{2,12,12} of size 1152
{2,12,3} of size 1152
{2,12,12} of size 1152
{2,12,10} of size 1200
{2,12,26} of size 1248
{2,12,6} of size 1296
{2,12,12} of size 1296
{2,12,3} of size 1296
{2,12,9} of size 1296
{2,12,9} of size 1296
{2,12,28} of size 1344
{2,12,21} of size 1344
{2,12,30} of size 1440
{2,12,30} of size 1440
{2,12,30} of size 1440
{2,12,6} of size 1440
{2,12,6} of size 1440
{2,12,10} of size 1440
{2,12,15} of size 1440
{2,12,30} of size 1440
{2,12,34} of size 1632
{2,12,36} of size 1728
{2,12,36} of size 1728
{2,12,12} of size 1728
{2,12,12} of size 1728
{2,12,12} of size 1728
{2,12,9} of size 1728
{2,12,3} of size 1728
{2,12,4} of size 1728
{2,12,4} of size 1728
{2,12,12} of size 1728
{2,12,12} of size 1728
{2,12,12} of size 1728
{2,12,12} of size 1728
{2,12,12} of size 1728
{2,12,18} of size 1728
{2,12,18} of size 1728
{2,12,6} of size 1728
{2,12,6} of size 1728
{2,12,4} of size 1728
{2,12,4} of size 1728
{2,12,12} of size 1728
{2,12,12} of size 1728
{2,12,12} of size 1728
{2,12,12} of size 1728
{2,12,12} of size 1728
{2,12,12} of size 1728
{2,12,12} of size 1728
{2,12,6} of size 1728
{2,12,38} of size 1824
{2,12,40} of size 1920
{2,12,40} of size 1920
{2,12,20} of size 1920
{2,12,20} of size 1920
{2,12,30} of size 1920
{2,12,20} of size 1920
{2,12,30} of size 1920
{2,12,10} of size 1920
{2,12,4} of size 1920
{2,12,6} of size 1920
{2,12,10} of size 1920
{2,12,4} of size 1920
{2,12,10} of size 1920
{2,12,10} of size 1920
{2,12,6} of size 1920
{2,12,10} of size 1920
Vertex Figure Of :
{2,2,12} of size 96
{3,2,12} of size 144
{4,2,12} of size 192
{5,2,12} of size 240
{6,2,12} of size 288
{7,2,12} of size 336
{8,2,12} of size 384
{9,2,12} of size 432
{10,2,12} of size 480
{11,2,12} of size 528
{12,2,12} of size 576
{13,2,12} of size 624
{14,2,12} of size 672
{15,2,12} of size 720
{16,2,12} of size 768
{17,2,12} of size 816
{18,2,12} of size 864
{19,2,12} of size 912
{20,2,12} of size 960
{21,2,12} of size 1008
{22,2,12} of size 1056
{23,2,12} of size 1104
{24,2,12} of size 1152
{25,2,12} of size 1200
{26,2,12} of size 1248
{27,2,12} of size 1296
{28,2,12} of size 1344
{29,2,12} of size 1392
{30,2,12} of size 1440
{31,2,12} of size 1488
{33,2,12} of size 1584
{34,2,12} of size 1632
{35,2,12} of size 1680
{36,2,12} of size 1728
{37,2,12} of size 1776
{38,2,12} of size 1824
{39,2,12} of size 1872
{40,2,12} of size 1920
{41,2,12} of size 1968
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,6}*24
3-fold quotients : {2,4}*16
4-fold quotients : {2,3}*12
6-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12}*96a, {2,24}*96
3-fold covers : {2,36}*144, {6,12}*144a, {6,12}*144b
4-fold covers : {4,24}*192a, {4,12}*192a, {4,24}*192b, {8,12}*192a, {8,12}*192b, {2,48}*192, {4,12}*192b
5-fold covers : {10,12}*240, {2,60}*240
6-fold covers : {4,36}*288a, {2,72}*288, {6,24}*288a, {6,24}*288b, {12,12}*288a, {12,12}*288b
7-fold covers : {14,12}*336, {2,84}*336
8-fold covers : {4,24}*384a, {8,24}*384a, {8,24}*384b, {8,12}*384a, {8,24}*384c, {8,24}*384d, {4,48}*384a, {4,48}*384b, {4,12}*384a, {4,24}*384b, {8,12}*384b, {16,12}*384a, {16,12}*384b, {2,96}*384, {4,12}*384d, {8,12}*384e, {8,12}*384f, {4,24}*384c, {4,24}*384d
9-fold covers : {2,108}*432, {6,36}*432a, {6,36}*432b, {18,12}*432a, {6,12}*432a, {6,12}*432b, {6,12}*432g, {6,12}*432i
10-fold covers : {10,24}*480, {20,12}*480, {4,60}*480a, {2,120}*480
11-fold covers : {22,12}*528, {2,132}*528
12-fold covers : {4,72}*576a, {4,36}*576a, {4,72}*576b, {8,36}*576a, {8,36}*576b, {2,144}*576, {6,48}*576a, {6,48}*576b, {24,12}*576a, {12,12}*576a, {12,12}*576b, {24,12}*576b, {12,24}*576c, {12,24}*576d, {24,12}*576c, {12,24}*576e, {12,24}*576f, {24,12}*576e, {4,36}*576b, {12,12}*576f, {12,12}*576g, {6,12}*576a, {6,12}*576b
13-fold covers : {26,12}*624, {2,156}*624
14-fold covers : {14,24}*672, {28,12}*672, {4,84}*672a, {2,168}*672
15-fold covers : {10,36}*720, {2,180}*720, {30,12}*720a, {30,12}*720b, {6,60}*720b, {6,60}*720c
16-fold covers : {8,24}*768a, {8,12}*768a, {8,24}*768b, {4,24}*768a, {8,24}*768c, {8,24}*768d, {16,12}*768a, {4,48}*768a, {16,12}*768b, {4,48}*768b, {8,48}*768a, {16,24}*768a, {8,48}*768b, {16,24}*768b, {16,24}*768c, {8,48}*768c, {8,48}*768d, {16,24}*768d, {16,24}*768e, {8,48}*768e, {8,48}*768f, {16,24}*768f, {32,12}*768a, {4,96}*768a, {32,12}*768b, {4,96}*768b, {4,12}*768a, {4,24}*768b, {8,12}*768b, {8,12}*768c, {8,24}*768e, {4,24}*768c, {4,24}*768d, {8,12}*768d, {8,24}*768f, {8,24}*768g, {8,24}*768h, {2,192}*768, {8,24}*768i, {8,24}*768j, {8,24}*768k, {8,24}*768l, {4,12}*768b, {8,12}*768q, {8,12}*768r, {8,12}*768s, {4,24}*768i, {4,12}*768d, {8,12}*768t, {4,24}*768j, {8,12}*768u, {4,12}*768e, {4,24}*768k, {8,12}*768w, {4,12}*768f, {4,24}*768l, {4,48}*768c, {4,48}*768d
17-fold covers : {34,12}*816, {2,204}*816
18-fold covers : {4,108}*864a, {2,216}*864, {6,72}*864a, {6,72}*864b, {18,24}*864a, {6,24}*864a, {6,24}*864b, {12,36}*864a, {12,36}*864b, {36,12}*864a, {12,12}*864b, {12,12}*864c, {6,24}*864f, {12,12}*864h, {4,12}*864c, {4,12}*864d, {6,24}*864h, {12,12}*864l
19-fold covers : {38,12}*912, {2,228}*912
20-fold covers : {10,48}*960, {20,12}*960a, {20,24}*960a, {40,12}*960a, {20,24}*960b, {40,12}*960b, {4,120}*960a, {4,60}*960a, {4,120}*960b, {8,60}*960a, {8,60}*960b, {2,240}*960, {20,12}*960b, {4,60}*960b
21-fold covers : {14,36}*1008, {2,252}*1008, {42,12}*1008a, {42,12}*1008b, {6,84}*1008b, {6,84}*1008c
22-fold covers : {22,24}*1056, {44,12}*1056, {4,132}*1056a, {2,264}*1056
23-fold covers : {46,12}*1104, {2,276}*1104
24-fold covers : {8,36}*1152a, {4,72}*1152a, {12,24}*1152a, {12,24}*1152b, {24,12}*1152b, {24,12}*1152c, {8,72}*1152a, {8,72}*1152b, {8,72}*1152c, {24,24}*1152a, {24,24}*1152b, {24,24}*1152f, {24,24}*1152g, {24,24}*1152h, {24,24}*1152i, {8,72}*1152d, {24,24}*1152j, {24,24}*1152k, {16,36}*1152a, {4,144}*1152a, {12,48}*1152a, {12,48}*1152b, {48,12}*1152b, {48,12}*1152c, {16,36}*1152b, {4,144}*1152b, {12,48}*1152d, {12,48}*1152e, {48,12}*1152e, {48,12}*1152f, {4,36}*1152a, {4,72}*1152b, {8,36}*1152b, {12,12}*1152b, {12,24}*1152e, {24,12}*1152d, {24,12}*1152e, {12,12}*1152c, {12,24}*1152f, {2,288}*1152, {6,96}*1152b, {6,96}*1152c, {4,36}*1152d, {8,36}*1152e, {8,36}*1152f, {4,72}*1152c, {4,72}*1152d, {24,12}*1152i, {24,12}*1152j, {24,12}*1152k, {24,12}*1152l, {12,12}*1152f, {6,12}*1152a, {6,24}*1152d, {12,24}*1152o, {12,24}*1152p, {12,24}*1152q, {12,24}*1152r, {6,24}*1152g, {6,24}*1152h, {6,12}*1152d, {6,24}*1152i, {12,12}*1152h, {12,12}*1152j, {12,12}*1152k, {12,12}*1152n, {12,12}*1152o
25-fold covers : {50,12}*1200, {2,300}*1200, {10,12}*1200a, {10,12}*1200b, {10,60}*1200a, {10,60}*1200b, {10,60}*1200c, {10,12}*1200c
26-fold covers : {26,24}*1248, {52,12}*1248, {4,156}*1248a, {2,312}*1248
27-fold covers : {2,324}*1296, {18,36}*1296a, {18,36}*1296b, {18,12}*1296a, {6,36}*1296a, {6,36}*1296b, {54,12}*1296a, {6,108}*1296a, {6,108}*1296b, {6,12}*1296a, {6,36}*1296c, {6,12}*1296b, {6,36}*1296d, {18,12}*1296b, {6,36}*1296e, {6,36}*1296f, {18,12}*1296c, {18,12}*1296d, {6,12}*1296c, {6,36}*1296g, {6,36}*1296l, {18,12}*1296l, {6,12}*1296g, {6,12}*1296h, {6,12}*1296i, {6,36}*1296m, {6,12}*1296o, {6,36}*1296n, {6,36}*1296o, {6,12}*1296t, {6,12}*1296u
28-fold covers : {14,48}*1344, {28,12}*1344a, {28,24}*1344a, {56,12}*1344a, {28,24}*1344b, {56,12}*1344b, {4,168}*1344a, {4,84}*1344a, {4,168}*1344b, {8,84}*1344a, {8,84}*1344b, {2,336}*1344, {28,12}*1344b, {4,84}*1344b
29-fold covers : {58,12}*1392, {2,348}*1392
30-fold covers : {10,72}*1440, {20,36}*1440, {4,180}*1440a, {2,360}*1440, {30,24}*1440a, {60,12}*1440a, {30,24}*1440b, {6,120}*1440b, {6,120}*1440c, {12,60}*1440b, {12,60}*1440c, {60,12}*1440b
31-fold covers : {62,12}*1488, {2,372}*1488
33-fold covers : {22,36}*1584, {2,396}*1584, {66,12}*1584a, {66,12}*1584b, {6,132}*1584b, {6,132}*1584c
34-fold covers : {34,24}*1632, {68,12}*1632, {4,204}*1632a, {2,408}*1632
35-fold covers : {14,60}*1680, {10,84}*1680, {70,12}*1680, {2,420}*1680
36-fold covers : {4,216}*1728a, {4,108}*1728a, {4,216}*1728b, {8,108}*1728a, {8,108}*1728b, {2,432}*1728, {6,144}*1728a, {6,144}*1728b, {18,48}*1728a, {6,48}*1728a, {6,48}*1728b, {24,36}*1728a, {24,12}*1728a, {12,36}*1728a, {12,36}*1728b, {36,12}*1728a, {12,12}*1728b, {12,12}*1728c, {24,36}*1728b, {24,12}*1728b, {12,72}*1728a, {12,72}*1728b, {72,12}*1728a, {24,36}*1728c, {36,24}*1728c, {12,24}*1728c, {12,24}*1728d, {24,12}*1728d, {12,72}*1728c, {12,72}*1728d, {72,12}*1728c, {24,36}*1728d, {36,24}*1728d, {12,24}*1728e, {12,24}*1728f, {24,12}*1728f, {4,108}*1728b, {6,48}*1728f, {12,24}*1728o, {24,12}*1728o, {12,24}*1728p, {24,12}*1728p, {12,12}*1728h, {36,12}*1728c, {6,36}*1728a, {6,36}*1728b, {12,36}*1728e, {12,36}*1728f, {18,12}*1728c, {12,12}*1728k, {12,12}*1728l, {6,12}*1728a, {6,12}*1728b, {4,24}*1728e, {4,24}*1728f, {8,12}*1728e, {4,24}*1728g, {4,24}*1728h, {8,12}*1728f, {8,12}*1728g, {8,12}*1728h, {4,12}*1728c, {4,12}*1728d, {6,48}*1728h, {12,12}*1728t, {12,24}*1728u, {24,12}*1728v, {24,12}*1728w, {12,24}*1728x, {12,12}*1728w, {6,12}*1728h, {6,12}*1728i, {12,12}*1728ab
37-fold covers : {74,12}*1776, {2,444}*1776
38-fold covers : {38,24}*1824, {76,12}*1824, {4,228}*1824a, {2,456}*1824
39-fold covers : {26,36}*1872, {2,468}*1872, {78,12}*1872a, {78,12}*1872b, {6,156}*1872b, {6,156}*1872c
40-fold covers : {8,60}*1920a, {4,120}*1920a, {40,12}*1920a, {20,24}*1920a, {8,120}*1920a, {8,120}*1920b, {8,120}*1920c, {40,24}*1920a, {40,24}*1920b, {40,24}*1920c, {8,120}*1920d, {40,24}*1920d, {16,60}*1920a, {4,240}*1920a, {80,12}*1920a, {20,48}*1920a, {16,60}*1920b, {4,240}*1920b, {80,12}*1920b, {20,48}*1920b, {4,60}*1920a, {4,120}*1920b, {8,60}*1920b, {40,12}*1920b, {20,24}*1920b, {20,12}*1920a, {2,480}*1920, {10,96}*1920, {40,12}*1920e, {40,12}*1920f, {20,24}*1920c, {20,24}*1920d, {20,12}*1920c, {4,60}*1920d, {8,60}*1920e, {8,60}*1920f, {4,120}*1920c, {4,120}*1920d
41-fold covers : {82,12}*1968, {2,492}*1968
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 9,12)(10,11)(13,14);;
s2 := ( 3, 9)( 4, 6)( 5,13)( 7,10)( 8,11)(12,14);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(14)!(1,2);
s1 := Sym(14)!( 4, 5)( 6, 7)( 9,12)(10,11)(13,14);
s2 := Sym(14)!( 3, 9)( 4, 6)( 5,13)( 7,10)( 8,11)(12,14);
poly := sub<Sym(14)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope