Polytope of Type {12,4,2,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,2,3,2}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157549)
Rank : 6
Schlafli Type : {12,4,2,3,2}
Number of vertices, edges, etc : 12, 24, 4, 3, 3, 2
Order of s₀s₁s₂s₃s₄s₅ : 12
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 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) :
   2-fold quotients : {6,4,2,3,2}*576c
   4-fold quotients : {3,4,2,3,2}*288
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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