Polytope of Type {2,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4}*1152
if this polytope has a name.
Group : SmallGroup(1152,99277)
Rank : 4
Schlafli Type : {2,4,4}
Number of vertices, edges, etc : 2, 72, 144, 72
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 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 : {2,4,4}*576
   4-fold quotients : {2,4,4}*288
   8-fold quotients : {2,4,4}*144
   9-fold quotients : {2,4,4}*128
   18-fold quotients : {2,4,4}*64
   36-fold quotients : {2,2,4}*32, {2,4,2}*32
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(21,30)(22,31)(23,32)(24,36)
(25,37)(26,38)(27,33)(28,34)(29,35)(42,45)(43,46)(44,47)(51,54)(52,55)(53,56)
(57,66)(58,67)(59,68)(60,72)(61,73)(62,74)(63,69)(64,70)(65,71);;
s2 := ( 4, 6)( 5, 9)( 8,10)(13,15)(14,18)(17,19)(22,24)(23,27)(26,28)(31,33)
(32,36)(35,37)(39,57)(40,60)(41,63)(42,58)(43,61)(44,64)(45,59)(46,62)(47,65)
(48,66)(49,69)(50,72)(51,67)(52,70)(53,73)(54,68)(55,71)(56,74);;
s3 := ( 3,49)( 4,48)( 5,50)( 6,52)( 7,51)( 8,53)( 9,55)(10,54)(11,56)(12,40)
(13,39)(14,41)(15,43)(16,42)(17,44)(18,46)(19,45)(20,47)(21,58)(22,57)(23,59)
(24,61)(25,60)(26,62)(27,64)(28,63)(29,65)(30,67)(31,66)(32,68)(33,70)(34,69)
(35,71)(36,73)(37,72)(38,74);;
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(21,30)(22,31)(23,32)
(24,36)(25,37)(26,38)(27,33)(28,34)(29,35)(42,45)(43,46)(44,47)(51,54)(52,55)
(53,56)(57,66)(58,67)(59,68)(60,72)(61,73)(62,74)(63,69)(64,70)(65,71);
s2 := Sym(74)!( 4, 6)( 5, 9)( 8,10)(13,15)(14,18)(17,19)(22,24)(23,27)(26,28)
(31,33)(32,36)(35,37)(39,57)(40,60)(41,63)(42,58)(43,61)(44,64)(45,59)(46,62)
(47,65)(48,66)(49,69)(50,72)(51,67)(52,70)(53,73)(54,68)(55,71)(56,74);
s3 := Sym(74)!( 3,49)( 4,48)( 5,50)( 6,52)( 7,51)( 8,53)( 9,55)(10,54)(11,56)
(12,40)(13,39)(14,41)(15,43)(16,42)(17,44)(18,46)(19,45)(20,47)(21,58)(22,57)
(23,59)(24,61)(25,60)(26,62)(27,64)(28,63)(29,65)(30,67)(31,66)(32,68)(33,70)
(34,69)(35,71)(36,73)(37,72)(38,74);
poly := sub<Sym(74)|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, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;

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