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

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

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

Permutation Representation (Magma) :

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

to this polytope