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Polytope of Type {12,6,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,2,4}*1152c
if this polytope has a name.
Group : SmallGroup(1152,136342)
Rank : 5
Schlafli Type : {12,6,2,4}
Number of vertices, edges, etc : 12, 36, 6, 4, 4
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 : {12,6,2,2}*576b, {6,6,2,4}*576c
   3-fold quotients : {12,2,2,4}*384
   4-fold quotients : {3,6,2,4}*288, {6,6,2,2}*288c
   6-fold quotients : {12,2,2,2}*192, {6,2,2,4}*192
   8-fold quotients : {3,6,2,2}*144
   9-fold quotients : {4,2,2,4}*128
   12-fold quotients : {3,2,2,4}*96, {6,2,2,2}*96
   18-fold quotients : {2,2,2,4}*64, {4,2,2,2}*64
   24-fold quotients : {3,2,2,2}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,37)( 2,39)( 3,38)( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,46)
(11,48)(12,47)(13,52)(14,54)(15,53)(16,49)(17,51)(18,50)(19,64)(20,66)(21,65)
(22,70)(23,72)(24,71)(25,67)(26,69)(27,68)(28,55)(29,57)(30,56)(31,61)(32,63)
(33,62)(34,58)(35,60)(36,59);;
s1 := ( 1,59)( 2,58)( 3,60)( 4,56)( 5,55)( 6,57)( 7,62)( 8,61)( 9,63)(10,68)
(11,67)(12,69)(13,65)(14,64)(15,66)(16,71)(17,70)(18,72)(19,41)(20,40)(21,42)
(22,38)(23,37)(24,39)(25,44)(26,43)(27,45)(28,50)(29,49)(30,51)(31,47)(32,46)
(33,48)(34,53)(35,52)(36,54);;
s2 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)
(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)
(65,66)(68,69)(71,72);;
s3 := (74,75);;
s4 := (73,74)(75,76);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*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*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(76)!( 1,37)( 2,39)( 3,38)( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)
(10,46)(11,48)(12,47)(13,52)(14,54)(15,53)(16,49)(17,51)(18,50)(19,64)(20,66)
(21,65)(22,70)(23,72)(24,71)(25,67)(26,69)(27,68)(28,55)(29,57)(30,56)(31,61)
(32,63)(33,62)(34,58)(35,60)(36,59);
s1 := Sym(76)!( 1,59)( 2,58)( 3,60)( 4,56)( 5,55)( 6,57)( 7,62)( 8,61)( 9,63)
(10,68)(11,67)(12,69)(13,65)(14,64)(15,66)(16,71)(17,70)(18,72)(19,41)(20,40)
(21,42)(22,38)(23,37)(24,39)(25,44)(26,43)(27,45)(28,50)(29,49)(30,51)(31,47)
(32,46)(33,48)(34,53)(35,52)(36,54);
s2 := Sym(76)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)
(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)
(62,63)(65,66)(68,69)(71,72);
s3 := Sym(76)!(74,75);
s4 := Sym(76)!(73,74)(75,76);
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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s2*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*s0*s1 >; 
 

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