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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,8,6}*384
if this polytope has a name.
Group : SmallGroup(384,19745)
Rank : 5
Schlafli Type : {2,2,8,6}
Number of vertices, edges, etc : 2, 2, 8, 24, 6
Order of s₀s₁s₂s₃s₄ : 24
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,8,6,2} of size 768
   {2,2,8,6,3} of size 1152
Vertex Figure Of :
   {2,2,2,8,6} of size 768
   {3,2,2,8,6} of size 1152
   {5,2,2,8,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,4,6}*192a
   3-fold quotients : {2,2,8,2}*128
   4-fold quotients : {2,2,2,6}*96
   6-fold quotients : {2,2,4,2}*64
   8-fold quotients : {2,2,2,3}*48
   12-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,8,6}*768a, {2,2,8,12}*768a, {4,2,8,6}*768, {2,2,16,6}*768
   3-fold covers : {2,2,8,18}*1152, {2,6,8,6}*1152, {6,2,8,6}*1152, {2,2,24,6}*1152a, {2,2,24,6}*1152b
   5-fold covers : {2,2,8,30}*1920, {2,10,8,6}*1920, {10,2,8,6}*1920, {2,2,40,6}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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