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Polytope of Type {6,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,155790)
Rank : 4
Schlafli Type : {6,6,4}
Number of vertices, edges, etc : 6, 72, 48, 16
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Non-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) :
   3-fold quotients : {2,6,4}*384a
   4-fold quotients : {6,6,4}*288e
   8-fold quotients : {6,3,4}*144
   12-fold quotients : {2,6,4}*96c
   24-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (17,33)(18,34)(19,35)(20,36)(21,37)(22,38)(23,39)(24,40)(25,41)(26,42)
(27,43)(28,44)(29,45)(30,46)(31,47)(32,48);;
s1 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,21)( 6,22)( 7,24)( 8,23)( 9,29)(10,30)
(11,32)(12,31)(13,25)(14,26)(15,28)(16,27)(35,36)(39,40)(41,45)(42,46)(43,48)
(44,47);;
s2 := ( 2, 4)( 5,16)( 6,13)( 7,14)( 8,15)( 9,11)(17,33)(18,36)(19,35)(20,34)
(21,48)(22,45)(23,46)(24,47)(25,43)(26,42)(27,41)(28,44)(29,38)(30,39)(31,40)
(32,37);;
s3 := ( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9,13)(10,14)(11,15)(12,16)(17,21)(18,22)
(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)(33,37)(34,38)(35,39)(36,40)(41,45)
(42,46)(43,47)(44,48);;
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*s2*s3*s2*s3, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(48)!(17,33)(18,34)(19,35)(20,36)(21,37)(22,38)(23,39)(24,40)(25,41)
(26,42)(27,43)(28,44)(29,45)(30,46)(31,47)(32,48);
s1 := Sym(48)!( 1,17)( 2,18)( 3,20)( 4,19)( 5,21)( 6,22)( 7,24)( 8,23)( 9,29)
(10,30)(11,32)(12,31)(13,25)(14,26)(15,28)(16,27)(35,36)(39,40)(41,45)(42,46)
(43,48)(44,47);
s2 := Sym(48)!( 2, 4)( 5,16)( 6,13)( 7,14)( 8,15)( 9,11)(17,33)(18,36)(19,35)
(20,34)(21,48)(22,45)(23,46)(24,47)(25,43)(26,42)(27,41)(28,44)(29,38)(30,39)
(31,40)(32,37);
s3 := Sym(48)!( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9,13)(10,14)(11,15)(12,16)(17,21)
(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)(33,37)(34,38)(35,39)(36,40)
(41,45)(42,46)(43,47)(44,48);
poly := sub<Sym(48)|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*s2*s3*s2*s3, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3 >; 
 
References : None.
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