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Polytope of Type {2,2,12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,12,12}*1152c
if this polytope has a name.
Group : SmallGroup(1152,134272)
Rank : 5
Schlafli Type : {2,2,12,12}
Number of vertices, edges, etc : 2, 2, 12, 72, 12
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,12,6}*576b, {2,2,6,12}*576c
   3-fold quotients : {2,2,12,4}*384a
   4-fold quotients : {2,2,6,6}*288c
   6-fold quotients : {2,2,12,2}*192, {2,2,6,4}*192a
   8-fold quotients : {2,2,3,6}*144
   9-fold quotients : {2,2,4,4}*128
   12-fold quotients : {2,2,6,2}*96
   18-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   24-fold quotients : {2,2,3,2}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8,11)( 9,13)(10,12)(15,16)(17,20)(18,22)(19,21)(24,25)(26,29)
(27,31)(28,30)(33,34)(35,38)(36,40)(37,39)(41,68)(42,70)(43,69)(44,74)(45,76)
(46,75)(47,71)(48,73)(49,72)(50,59)(51,61)(52,60)(53,65)(54,67)(55,66)(56,62)
(57,64)(58,63);;
s3 := ( 5,45)( 6,44)( 7,46)( 8,42)( 9,41)(10,43)(11,48)(12,47)(13,49)(14,54)
(15,53)(16,55)(17,51)(18,50)(19,52)(20,57)(21,56)(22,58)(23,63)(24,62)(25,64)
(26,60)(27,59)(28,61)(29,66)(30,65)(31,67)(32,72)(33,71)(34,73)(35,69)(36,68)
(37,70)(38,75)(39,74)(40,76);;
s4 := ( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31)(35,38)
(36,39)(37,40)(41,59)(42,60)(43,61)(44,65)(45,66)(46,67)(47,62)(48,63)(49,64)
(50,68)(51,69)(52,70)(53,74)(54,75)(55,76)(56,71)(57,72)(58,73);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(76)!(1,2);
s1 := Sym(76)!(3,4);
s2 := Sym(76)!( 6, 7)( 8,11)( 9,13)(10,12)(15,16)(17,20)(18,22)(19,21)(24,25)
(26,29)(27,31)(28,30)(33,34)(35,38)(36,40)(37,39)(41,68)(42,70)(43,69)(44,74)
(45,76)(46,75)(47,71)(48,73)(49,72)(50,59)(51,61)(52,60)(53,65)(54,67)(55,66)
(56,62)(57,64)(58,63);
s3 := Sym(76)!( 5,45)( 6,44)( 7,46)( 8,42)( 9,41)(10,43)(11,48)(12,47)(13,49)
(14,54)(15,53)(16,55)(17,51)(18,50)(19,52)(20,57)(21,56)(22,58)(23,63)(24,62)
(25,64)(26,60)(27,59)(28,61)(29,66)(30,65)(31,67)(32,72)(33,71)(34,73)(35,69)
(36,68)(37,70)(38,75)(39,74)(40,76);
s4 := Sym(76)!( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31)
(35,38)(36,39)(37,40)(41,59)(42,60)(43,61)(44,65)(45,66)(46,67)(47,62)(48,63)
(49,64)(50,68)(51,69)(52,70)(53,74)(54,75)(55,76)(56,71)(57,72)(58,73);
poly := sub<Sym(76)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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