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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,2}*384
if this polytope has a name.
Group : SmallGroup(384,20162)
Rank : 5
Schlafli Type : {2,6,6,2}
Number of vertices, edges, etc : 2, 8, 24, 8, 2
Order of s₀s₁s₂s₃s₄ : 4
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,6,2,2} of size 768
   {2,6,6,2,3} of size 1152
   {2,6,6,2,5} of size 1920
Vertex Figure Of :
   {2,2,6,6,2} of size 768
   {3,2,6,6,2} of size 1152
   {5,2,6,6,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,6,2}*192, {2,6,3,2}*192
   4-fold quotients : {2,3,3,2}*96
   12-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,6,4}*768, {2,6,12,2}*768a, {2,12,6,2}*768a, {4,6,6,2}*768, {2,6,12,2}*768b, {2,12,6,2}*768b, {2,6,6,2}*768b
   3-fold covers : {2,6,6,2}*1152a, {2,6,6,2}*1152b, {2,6,6,6}*1152b, {6,6,6,2}*1152a
   5-fold covers : {2,6,6,10}*1920, {2,6,30,2}*1920, {2,30,6,2}*1920, {10,6,6,2}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope