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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,12,2}*768c
if this polytope has a name.
Group : SmallGroup(768,1090143)
Rank : 6
Schlafli Type : {2,2,4,12,2}
Number of vertices, edges, etc : 2, 2, 4, 24, 12, 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 : {2,2,4,6,2}*384c
   4-fold quotients : {2,2,4,3,2}*192
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5,25)( 6,17)( 7,14)( 8,39)( 9,40)(10,11)(12,31)(13,32)(15,26)(16,27)
(18,23)(19,24)(20,51)(21,52)(22,50)(28,46)(29,48)(30,44)(33,49)(34,47)(35,45)
(36,43)(37,41)(38,42);;
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);;
s5 := (53,54);;
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*s1*s0*s1, 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*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, 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(54)!(1,2);
s1 := Sym(54)!(3,4);
s2 := Sym(54)!( 5,25)( 6,17)( 7,14)( 8,39)( 9,40)(10,11)(12,31)(13,32)(15,26)
(16,27)(18,23)(19,24)(20,51)(21,52)(22,50)(28,46)(29,48)(30,44)(33,49)(34,47)
(35,45)(36,43)(37,41)(38,42);
s3 := Sym(54)!( 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(54)!( 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);
s5 := Sym(54)!(53,54);
poly := sub<Sym(54)|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*s1*s0*s1, 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*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, 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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