Polytope of Type {2,2,4,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,6,6}*1152b
if this polytope has a name.
Group : SmallGroup(1152,153175)
Rank : 6
Schlafli Type : {2,2,4,6,6}
Number of vertices, edges, etc : 2, 2, 4, 12, 18, 6
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 : {2,2,2,6,6}*576c
   3-fold quotients : {2,2,4,6,2}*384a
   4-fold quotients : {2,2,2,3,6}*288
   6-fold quotients : {2,2,2,6,2}*192
   9-fold quotients : {2,2,4,2,2}*128
   12-fold quotients : {2,2,2,3,2}*96
   18-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(31,40);;
s3 := ( 5,23)( 6,25)( 7,24)( 8,29)( 9,31)(10,30)(11,26)(12,28)(13,27)(14,32)
(15,34)(16,33)(17,38)(18,40)(19,39)(20,35)(21,37)(22,36);;
s4 := ( 5, 9)( 6, 8)( 7,10)(11,12)(14,18)(15,17)(16,19)(20,21)(23,27)(24,26)
(25,28)(29,30)(32,36)(33,35)(34,37)(38,39);;
s5 := ( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31)(35,38)
(36,39)(37,40);;
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*s1*s0*s1, 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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s3*s4*s5*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(40)!(1,2);
s1 := Sym(40)!(3,4);
s2 := Sym(40)!(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(31,40);
s3 := Sym(40)!( 5,23)( 6,25)( 7,24)( 8,29)( 9,31)(10,30)(11,26)(12,28)(13,27)
(14,32)(15,34)(16,33)(17,38)(18,40)(19,39)(20,35)(21,37)(22,36);
s4 := Sym(40)!( 5, 9)( 6, 8)( 7,10)(11,12)(14,18)(15,17)(16,19)(20,21)(23,27)
(24,26)(25,28)(29,30)(32,36)(33,35)(34,37)(38,39);
s5 := Sym(40)!( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(26,29)(27,30)(28,31)
(35,38)(36,39)(37,40);
poly := sub<Sym(40)|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*s1*s0*s1, 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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s5*s3*s4*s5*s4*s5*s3*s4*s5*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s3*s4*s5*s4*s3*s4 >;

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