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Polytope of Type {2,36,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,36,6}*1296b
if this polytope has a name.
Group : SmallGroup(1296,2978)
Rank : 4
Schlafli Type : {2,36,6}
Number of vertices, edges, etc : 2, 54, 162, 9
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   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 : {2,12,6}*432c
   9-fold quotients : {2,4,6}*144
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6,10)( 7, 9)( 8,11)(12,68)(13,67)(14,66)(15,72)(16,74)(17,73)
(18,69)(19,71)(20,70)(21,48)(22,50)(23,49)(24,55)(25,54)(26,56)(27,52)(28,51)
(29,53)(30,57)(31,59)(32,58)(33,64)(34,63)(35,65)(36,61)(37,60)(38,62)(39,41)
(42,45)(43,47)(44,46)(76,77)(78,82)(79,81)(80,83);;
s2 := ( 3, 6)( 4, 8)( 5, 7)( 9,10)(12,16)(13,15)(14,17)(18,20)(21,26)(22,25)
(23,24)(28,29)(30,78)(31,80)(32,79)(33,75)(34,77)(35,76)(36,82)(37,81)(38,83)
(39,61)(40,60)(41,62)(42,58)(43,57)(44,59)(45,65)(46,64)(47,63)(48,71)(49,70)
(50,69)(51,68)(52,67)(53,66)(54,72)(55,74)(56,73);;
s3 := ( 3,40)( 4,41)( 5,39)( 6,43)( 7,44)( 8,42)( 9,46)(10,47)(11,45)(12,32)
(13,30)(14,31)(15,35)(16,33)(17,34)(18,38)(19,36)(20,37)(21,48)(22,49)(23,50)
(24,51)(25,52)(26,53)(27,54)(28,55)(29,56)(57,67)(58,68)(59,66)(60,70)(61,71)
(62,69)(63,73)(64,74)(65,72);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s3*s2*s3*s2*s3*s2*s1*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(83)!(1,2);
s1 := Sym(83)!( 4, 5)( 6,10)( 7, 9)( 8,11)(12,68)(13,67)(14,66)(15,72)(16,74)
(17,73)(18,69)(19,71)(20,70)(21,48)(22,50)(23,49)(24,55)(25,54)(26,56)(27,52)
(28,51)(29,53)(30,57)(31,59)(32,58)(33,64)(34,63)(35,65)(36,61)(37,60)(38,62)
(39,41)(42,45)(43,47)(44,46)(76,77)(78,82)(79,81)(80,83);
s2 := Sym(83)!( 3, 6)( 4, 8)( 5, 7)( 9,10)(12,16)(13,15)(14,17)(18,20)(21,26)
(22,25)(23,24)(28,29)(30,78)(31,80)(32,79)(33,75)(34,77)(35,76)(36,82)(37,81)
(38,83)(39,61)(40,60)(41,62)(42,58)(43,57)(44,59)(45,65)(46,64)(47,63)(48,71)
(49,70)(50,69)(51,68)(52,67)(53,66)(54,72)(55,74)(56,73);
s3 := Sym(83)!( 3,40)( 4,41)( 5,39)( 6,43)( 7,44)( 8,42)( 9,46)(10,47)(11,45)
(12,32)(13,30)(14,31)(15,35)(16,33)(17,34)(18,38)(19,36)(20,37)(21,48)(22,49)
(23,50)(24,51)(25,52)(26,53)(27,54)(28,55)(29,56)(57,67)(58,68)(59,66)(60,70)
(61,71)(62,69)(63,73)(64,74)(65,72);
poly := sub<Sym(83)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s3*s2*s3*s2*s3*s2*s1*s2*s3 >; 
 

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