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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,4,12}*768b
if this polytope has a name.
Group : SmallGroup(768,1088766)
Rank : 5
Schlafli Type : {4,2,4,12}
Number of vertices, edges, etc : 4, 4, 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 :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,4,12}*384b, {4,2,4,6}*384c
   4-fold quotients : {4,2,4,3}*192, {2,2,4,6}*192c
   8-fold quotients : {2,2,4,3}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 5,10)( 6,14)( 7,17)( 8,18)( 9,19)(11,25)(12,26)(13,27)(15,31)(16,32)
(20,37)(21,38)(22,36)(23,39)(24,40)(28,49)(29,47)(30,45)(33,46)(34,48)(35,44)
(41,51)(42,52)(43,50);;
s3 := ( 6, 7)( 8, 9)(10,20)(12,16)(13,15)(14,28)(17,33)(18,36)(19,21)(22,38)
(23,24)(25,41)(26,44)(27,34)(29,32)(30,48)(31,45)(35,47)(39,50)(40,42)(43,52)
(46,49);;
s4 := ( 5,13)( 6, 9)( 7,24)( 8,12)(10,27)(11,16)(14,19)(15,23)(17,40)(18,26)
(20,30)(21,47)(22,33)(25,32)(28,43)(29,38)(31,39)(34,52)(35,41)(36,46)(37,45)
(42,48)(44,51)(49,50);;
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*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(52)!(2,3);
s1 := Sym(52)!(1,2)(3,4);
s2 := Sym(52)!( 5,10)( 6,14)( 7,17)( 8,18)( 9,19)(11,25)(12,26)(13,27)(15,31)
(16,32)(20,37)(21,38)(22,36)(23,39)(24,40)(28,49)(29,47)(30,45)(33,46)(34,48)
(35,44)(41,51)(42,52)(43,50);
s3 := Sym(52)!( 6, 7)( 8, 9)(10,20)(12,16)(13,15)(14,28)(17,33)(18,36)(19,21)
(22,38)(23,24)(25,41)(26,44)(27,34)(29,32)(30,48)(31,45)(35,47)(39,50)(40,42)
(43,52)(46,49);
s4 := Sym(52)!( 5,13)( 6, 9)( 7,24)( 8,12)(10,27)(11,16)(14,19)(15,23)(17,40)
(18,26)(20,30)(21,47)(22,33)(25,32)(28,43)(29,38)(31,39)(34,52)(35,41)(36,46)
(37,45)(42,48)(44,51)(49,50);
poly := sub<Sym(52)|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*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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