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Polytope of Type {2,2,6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,8}*768c
if this polytope has a name.
Group : SmallGroup(768,1090168)
Rank : 5
Schlafli Type : {2,2,6,8}
Number of vertices, edges, etc : 2, 2, 12, 48, 16
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,2,6,4}*384
   4-fold quotients : {2,2,3,4}*192, {2,2,6,4}*192b, {2,2,6,4}*192c
   8-fold quotients : {2,2,3,4}*96, {2,2,6,2}*96
   16-fold quotients : {2,2,3,2}*48
   24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 7, 9)( 8,10)(11,12)(13,14)(15,18)(16,17);;
s3 := ( 7, 8)( 9,11)(10,12)(15,16)(17,19)(18,20);;
s4 := ( 5,19)( 6,20)( 7,17)( 8,18)( 9,16)(10,15)(11,14)(12,13);;
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*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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s3*s4*s2*s3*s2*s3*s4*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(20)!(1,2);
s1 := Sym(20)!(3,4);
s2 := Sym(20)!( 7, 9)( 8,10)(11,12)(13,14)(15,18)(16,17);
s3 := Sym(20)!( 7, 8)( 9,11)(10,12)(15,16)(17,19)(18,20);
s4 := Sym(20)!( 5,19)( 6,20)( 7,17)( 8,18)( 9,16)(10,15)(11,14)(12,13);
poly := sub<Sym(20)|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*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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s3*s4*s2*s3*s2*s3*s4*s3*s2*s3 >; 
 

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