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Polytope of Type {4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12}*96b
if this polytope has a name.
Group : SmallGroup(96,187)
Rank : 3
Schlafli Type : {4,12}
Number of vertices, edges, etc : 4, 24, 12
Order of s0s1s2 : 12
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,12,2} of size 192
   {4,12,4} of size 384
   {4,12,4} of size 384
   {4,12,4} of size 384
   {4,12,6} of size 576
   {4,12,6} of size 576
   {4,12,6} of size 576
   {4,12,4} of size 768
   {4,12,8} of size 768
   {4,12,8} of size 768
   {4,12,4} of size 768
   {4,12,4} of size 768
   {4,12,6} of size 864
   {4,12,10} of size 960
   {4,12,12} of size 1152
   {4,12,12} of size 1152
   {4,12,6} of size 1152
   {4,12,14} of size 1344
   {4,12,18} of size 1728
   {4,12,6} of size 1728
   {4,12,6} of size 1728
   {4,12,18} of size 1728
   {4,12,6} of size 1728
   {4,12,6} of size 1728
   {4,12,4} of size 1728
   {4,12,6} of size 1728
   {4,12,20} of size 1920
Vertex Figure Of :
   {2,4,12} of size 192
   {4,4,12} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6}*48c
   4-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,24}*192c, {4,24}*192d, {4,12}*192b
   3-fold covers : {4,36}*288b
   4-fold covers : {4,12}*384b, {4,48}*384c, {4,48}*384d, {4,12}*384d, {8,12}*384e, {8,12}*384f, {4,24}*384c, {4,24}*384d
   5-fold covers : {4,60}*480b
   6-fold covers : {4,72}*576c, {4,72}*576d, {4,36}*576b, {12,12}*576f, {12,12}*576g
   7-fold covers : {4,84}*672b
   8-fold covers : {4,24}*768e, {4,24}*768f, {8,12}*768e, {8,12}*768f, {4,96}*768c, {4,96}*768d, {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
   9-fold covers : {4,108}*864b
   10-fold covers : {4,120}*960c, {4,120}*960d, {20,12}*960b, {4,60}*960b
   11-fold covers : {4,132}*1056b
   12-fold covers : {4,36}*1152b, {4,144}*1152c, {4,144}*1152d, {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, {12,24}*1152o, {12,24}*1152p, {12,24}*1152q, {12,24}*1152r, {12,12}*1152n, {12,12}*1152o
   13-fold covers : {4,156}*1248b
   14-fold covers : {4,168}*1344c, {4,168}*1344d, {28,12}*1344b, {4,84}*1344b
   15-fold covers : {4,180}*1440b
   17-fold covers : {4,204}*1632b
   18-fold covers : {4,216}*1728c, {4,216}*1728d, {4,108}*1728b, {36,12}*1728c, {12,36}*1728e, {12,36}*1728f, {12,12}*1728k, {12,12}*1728l, {12,12}*1728w, {12,12}*1728ab
   19-fold covers : {4,228}*1824b
   20-fold covers : {4,60}*1920b, {4,240}*1920c, {4,240}*1920d, {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
Permutation Representation (GAP) :
s0 := ( 1, 6)( 2,10)( 3,13)( 4,14)( 5,15)( 7,21)( 8,22)( 9,23)(11,27)(12,28)
(16,33)(17,34)(18,32)(19,35)(20,36)(24,45)(25,43)(26,41)(29,42)(30,44)(31,40)
(37,47)(38,48)(39,46);;
s1 := ( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)(18,34)
(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)(39,48)
(42,45);;
s2 := ( 1, 9)( 2, 5)( 3,20)( 4, 8)( 6,23)( 7,12)(10,15)(11,19)(13,36)(14,22)
(16,26)(17,43)(18,29)(21,28)(24,39)(25,34)(27,35)(30,48)(31,37)(32,42)(33,41)
(38,44)(40,47)(45,46);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, 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(48)!( 1, 6)( 2,10)( 3,13)( 4,14)( 5,15)( 7,21)( 8,22)( 9,23)(11,27)
(12,28)(16,33)(17,34)(18,32)(19,35)(20,36)(24,45)(25,43)(26,41)(29,42)(30,44)
(31,40)(37,47)(38,48)(39,46);
s1 := Sym(48)!( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)
(18,34)(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)
(39,48)(42,45);
s2 := Sym(48)!( 1, 9)( 2, 5)( 3,20)( 4, 8)( 6,23)( 7,12)(10,15)(11,19)(13,36)
(14,22)(16,26)(17,43)(18,29)(21,28)(24,39)(25,34)(27,35)(30,48)(31,37)(32,42)
(33,41)(38,44)(40,47)(45,46);
poly := sub<Sym(48)|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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 
References : None.
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