Polytope of Type {6,2,4,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,4,8}*768b
if this polytope has a name.
Group : SmallGroup(768,1036167)
Rank : 5
Schlafli Type : {6,2,4,8}
Number of vertices, edges, etc : 6, 6, 4, 16, 8
Order of s₀s₁s₂s₃s₄ : 24
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 : {3,2,4,8}*384b, {6,2,4,4}*384
   3-fold quotients : {2,2,4,8}*256b
   4-fold quotients : {3,2,4,4}*192, {6,2,2,4}*192, {6,2,4,2}*192
   6-fold quotients : {2,2,4,4}*128
   8-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96, {6,2,2,2}*96
   12-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   16-fold quotients : {3,2,2,2}*48
   24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8,10)( 9,12)(11,14)(15,18)(17,21)(19,20);;
s3 := ( 7, 8)( 9,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,22);;
s4 := ( 8, 9)(10,12)(11,14)(13,16)(17,20)(19,21);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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