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Polytope of Type {6,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,2}*864e
if this polytope has a name.
Group : SmallGroup(864,4007)
Rank : 4
Schlafli Type : {6,12,2}
Number of vertices, edges, etc : 18, 108, 36, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,12,2,2} of size 1728
Vertex Figure Of :
   {2,6,12,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,12,2}*432a
   3-fold quotients : {6,4,2}*288
   6-fold quotients : {6,4,2}*144
   27-fold quotients : {2,4,2}*32
   54-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,24,2}*1728d, {6,12,4}*1728i, {12,12,2}*1728g
Permutation Representation (GAP) :
s0 := ( 1,28)( 2,29)( 3,30)( 4,34)( 5,35)( 6,36)( 7,31)( 8,32)( 9,33)(10,46)
(11,47)(12,48)(13,52)(14,53)(15,54)(16,49)(17,50)(18,51)(19,37)(20,38)(21,39)
(22,43)(23,44)(24,45)(25,40)(26,41)(27,42);;
s1 := ( 1,10)( 2,12)( 3,11)( 4,14)( 5,13)( 6,15)( 7,18)( 8,17)( 9,16)(20,21)
(22,23)(25,27)(28,37)(29,39)(30,38)(31,41)(32,40)(33,42)(34,45)(35,44)(36,43)
(47,48)(49,50)(52,54);;
s2 := ( 2, 3)( 4,10)( 5,12)( 6,11)( 7,19)( 8,21)( 9,20)(13,14)(16,24)(17,23)
(18,22)(25,26)(29,30)(31,37)(32,39)(33,38)(34,46)(35,48)(36,47)(40,41)(43,51)
(44,50)(45,49)(52,53);;
s3 := (55,56);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(56)!( 1,28)( 2,29)( 3,30)( 4,34)( 5,35)( 6,36)( 7,31)( 8,32)( 9,33)
(10,46)(11,47)(12,48)(13,52)(14,53)(15,54)(16,49)(17,50)(18,51)(19,37)(20,38)
(21,39)(22,43)(23,44)(24,45)(25,40)(26,41)(27,42);
s1 := Sym(56)!( 1,10)( 2,12)( 3,11)( 4,14)( 5,13)( 6,15)( 7,18)( 8,17)( 9,16)
(20,21)(22,23)(25,27)(28,37)(29,39)(30,38)(31,41)(32,40)(33,42)(34,45)(35,44)
(36,43)(47,48)(49,50)(52,54);
s2 := Sym(56)!( 2, 3)( 4,10)( 5,12)( 6,11)( 7,19)( 8,21)( 9,20)(13,14)(16,24)
(17,23)(18,22)(25,26)(29,30)(31,37)(32,39)(33,38)(34,46)(35,48)(36,47)(40,41)
(43,51)(44,50)(45,49)(52,53);
s3 := Sym(56)!(55,56);
poly := sub<Sym(56)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1 >; 
 

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