Polytope of Type {2,6,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,28}*1008
if this polytope has a name.
Group : SmallGroup(1008,919)
Rank : 4
Schlafli Type : {2,6,28}
Number of vertices, edges, etc : 2, 9, 126, 42
Order of s₀s₁s₂s₃ : 28
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) :
   7-fold quotients : {2,6,4}*144
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (10,17)(11,18)(12,19)(13,20)(14,21)(15,22)(16,23)(24,45)(25,46)(26,47)
(27,48)(28,49)(29,50)(30,51)(31,59)(32,60)(33,61)(34,62)(35,63)(36,64)(37,65)
(38,52)(39,53)(40,54)(41,55)(42,56)(43,57)(44,58);;
s2 := ( 3,10)( 4,16)( 5,15)( 6,14)( 7,13)( 8,12)( 9,11)(18,23)(19,22)(20,21)
(24,31)(25,37)(26,36)(27,35)(28,34)(29,33)(30,32)(39,44)(40,43)(41,42)(45,52)
(46,58)(47,57)(48,56)(49,55)(50,54)(51,53)(60,65)(61,64)(62,63);;
s3 := ( 3, 4)( 5, 9)( 6, 8)(10,25)(11,24)(12,30)(13,29)(14,28)(15,27)(16,26)
(17,46)(18,45)(19,51)(20,50)(21,49)(22,48)(23,47)(31,32)(33,37)(34,36)(38,53)
(39,52)(40,58)(41,57)(42,56)(43,55)(44,54)(59,60)(61,65)(62,64);;
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, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2, 
s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(65)!(1,2);
s1 := Sym(65)!(10,17)(11,18)(12,19)(13,20)(14,21)(15,22)(16,23)(24,45)(25,46)
(26,47)(27,48)(28,49)(29,50)(30,51)(31,59)(32,60)(33,61)(34,62)(35,63)(36,64)
(37,65)(38,52)(39,53)(40,54)(41,55)(42,56)(43,57)(44,58);
s2 := Sym(65)!( 3,10)( 4,16)( 5,15)( 6,14)( 7,13)( 8,12)( 9,11)(18,23)(19,22)
(20,21)(24,31)(25,37)(26,36)(27,35)(28,34)(29,33)(30,32)(39,44)(40,43)(41,42)
(45,52)(46,58)(47,57)(48,56)(49,55)(50,54)(51,53)(60,65)(61,64)(62,63);
s3 := Sym(65)!( 3, 4)( 5, 9)( 6, 8)(10,25)(11,24)(12,30)(13,29)(14,28)(15,27)
(16,26)(17,46)(18,45)(19,51)(20,50)(21,49)(22,48)(23,47)(31,32)(33,37)(34,36)
(38,53)(39,52)(40,58)(41,57)(42,56)(43,55)(44,54)(59,60)(61,65)(62,64);
poly := sub<Sym(65)|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, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2, 
s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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