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