Polytope of Type {3,2,8,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,8,3,2}*1152
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 6
Schlafli Type : {3,2,8,3,2}
Number of vertices, edges, etc : 3, 3, 16, 24, 6, 2
Order of s₀s₁s₂s₃s₄s₅ : 12
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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) :
   2-fold quotients : {3,2,4,3,2}*576
   4-fold quotients : {3,2,4,3,2}*288
   8-fold quotients : {3,2,2,3,2}*144
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4,14)( 5,10)( 6, 9)( 7,30)( 8,32)(11,15)(12,19)(13,21)(16,18)(17,20)
(22,47)(23,51)(24,46)(25,49)(26,50)(27,48)(28,31)(29,33)(34,42)(35,44)(36,40)
(37,43)(38,45)(39,41);;
s3 := ( 5, 6)( 7, 8)( 9,22)(10,25)(12,17)(13,16)(14,34)(15,37)(18,40)(19,41)
(20,26)(21,23)(24,45)(27,44)(28,29)(30,46)(31,48)(32,35)(33,38)(36,50)(39,51)
(42,43);;
s4 := ( 4, 8)( 5,17)( 6,13)( 9,21)(10,20)(11,29)(12,16)(14,32)(15,33)(18,19)
(22,24)(23,45)(25,27)(26,44)(34,36)(35,50)(37,39)(38,51)(40,42)(41,43)(46,47)
(48,49);;
s5 := (52,53);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4, 
s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*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(53)!(2,3);
s1 := Sym(53)!(1,2);
s2 := Sym(53)!( 4,14)( 5,10)( 6, 9)( 7,30)( 8,32)(11,15)(12,19)(13,21)(16,18)
(17,20)(22,47)(23,51)(24,46)(25,49)(26,50)(27,48)(28,31)(29,33)(34,42)(35,44)
(36,40)(37,43)(38,45)(39,41);
s3 := Sym(53)!( 5, 6)( 7, 8)( 9,22)(10,25)(12,17)(13,16)(14,34)(15,37)(18,40)
(19,41)(20,26)(21,23)(24,45)(27,44)(28,29)(30,46)(31,48)(32,35)(33,38)(36,50)
(39,51)(42,43);
s4 := Sym(53)!( 4, 8)( 5,17)( 6,13)( 9,21)(10,20)(11,29)(12,16)(14,32)(15,33)
(18,19)(22,24)(23,45)(25,27)(26,44)(34,36)(35,50)(37,39)(38,51)(40,42)(41,43)
(46,47)(48,49);
s5 := Sym(53)!(52,53);
poly := sub<Sym(53)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4, 
s2*s4*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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