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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8,2,4}*768
if this polytope has a name.
Group : SmallGroup(768,1044755)
Rank : 5
Schlafli Type : {6,8,2,4}
Number of vertices, edges, etc : 6, 24, 8, 4, 4
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 : {6,4,2,4}*384a, {6,8,2,2}*384
   3-fold quotients : {2,8,2,4}*256
   4-fold quotients : {6,2,2,4}*192, {6,4,2,2}*192a
   6-fold quotients : {2,4,2,4}*128, {2,8,2,2}*128
   8-fold quotients : {3,2,2,4}*96, {6,2,2,2}*96
   12-fold quotients : {2,2,2,4}*64, {2,4,2,2}*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)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(23,24);;
s1 := ( 1, 3)( 2, 9)( 5, 6)( 7,10)( 8,15)(11,12)(13,16)(14,21)(17,18)(19,22)
(20,23);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5, 8)( 9,12)(10,13)(11,14)(15,18)(16,19)(17,20)
(21,23)(22,24);;
s3 := (26,27);;
s4 := (25,26)(27,28);;
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, 
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*s2*s1*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(28)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(23,24);
s1 := Sym(28)!( 1, 3)( 2, 9)( 5, 6)( 7,10)( 8,15)(11,12)(13,16)(14,21)(17,18)
(19,22)(20,23);
s2 := Sym(28)!( 1, 2)( 3, 6)( 4, 7)( 5, 8)( 9,12)(10,13)(11,14)(15,18)(16,19)
(17,20)(21,23)(22,24);
s3 := Sym(28)!(26,27);
s4 := Sym(28)!(25,26)(27,28);
poly := sub<Sym(28)|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, 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*s2*s1*s0*s1*s2*s1, 
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope