Polytope of Type {6,2,2,19}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,2,19}*912
if this polytope has a name.
Group : SmallGroup(912,213)
Rank : 5
Schlafli Type : {6,2,2,19}
Number of vertices, edges, etc : 6, 6, 2, 19, 19
Order of s₀s₁s₂s₃s₄ : 114
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,2,2,19,2} of size 1824
Vertex Figure Of :
   {2,6,2,2,19} of size 1824
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,2,19}*456
   3-fold quotients : {2,2,2,19}*304
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,2,2,19}*1824, {6,4,2,19}*1824a, {6,2,2,38}*1824
Permutation Representation (GAP) :

s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := (7,8);;
s3 := (10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27);;
s4 := ( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);;
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, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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(27)!(3,4)(5,6);
s1 := Sym(27)!(1,5)(2,3)(4,6);
s2 := Sym(27)!(7,8);
s3 := Sym(27)!(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27);
s4 := Sym(27)!( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);
poly := sub<Sym(27)|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, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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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