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Polytope of Type {2,6,36}

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

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