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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,12,3}*576
if this polytope has a name.
Group : SmallGroup(576,8340)
Rank : 5
Schlafli Type : {3,2,12,3}
Number of vertices, edges, etc : 3, 3, 16, 24, 4
Order of s₀s₁s₂s₃s₄ : 24
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,12,3,2} of size 1152
Vertex Figure Of :
   {2,3,2,12,3} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,6,3}*288
   4-fold quotients : {3,2,3,3}*144
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,12,6}*1152b, {6,2,12,3}*1152
   3-fold covers : {9,2,12,3}*1728, {3,2,12,3}*1728, {3,6,12,3}*1728
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4, 
s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

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