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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,12}*576c
if this polytope has a name.
Group : SmallGroup(576,8312)
Rank : 5
Schlafli Type : {3,2,4,12}
Number of vertices, edges, etc : 3, 3, 4, 24, 12
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,4,12,2} of size 1152
Vertex Figure Of :
   {2,3,2,4,12} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,4,6}*288c
   4-fold quotients : {3,2,4,3}*144
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,4,12}*1152b, {6,2,4,12}*1152c
   3-fold covers : {9,2,4,12}*1728c, {3,2,4,36}*1728c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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