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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,2,2}*288c
if this polytope has a name.
Group : SmallGroup(288,1040)
Rank : 5
Schlafli Type : {6,6,2,2}
Number of vertices, edges, etc : 6, 18, 6, 2, 2
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,6,2,2,2} of size 576
   {6,6,2,2,3} of size 864
   {6,6,2,2,4} of size 1152
   {6,6,2,2,5} of size 1440
   {6,6,2,2,6} of size 1728
Vertex Figure Of :
   {2,6,6,2,2} of size 576
   {4,6,6,2,2} of size 1152
   {4,6,6,2,2} of size 1152
   {4,6,6,2,2} of size 1152
   {6,6,6,2,2} of size 1728
   {6,6,6,2,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,6,2,2}*144
   3-fold quotients : {6,2,2,2}*96
   6-fold quotients : {3,2,2,2}*48
   9-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,6,2,2}*576b, {6,6,2,4}*576c, {6,6,4,2}*576c, {6,12,2,2}*576c
   3-fold covers : {18,6,2,2}*864b, {6,6,2,2}*864c, {6,6,2,2}*864d, {6,6,2,6}*864c, {6,6,6,2}*864g
   4-fold covers : {6,6,4,4}*1152c, {6,12,4,2}*1152c, {12,12,2,2}*1152c, {6,12,2,4}*1152a, {12,6,2,4}*1152c, {12,6,4,2}*1152c, {6,6,2,8}*1152c, {6,6,8,2}*1152c, {6,24,2,2}*1152a, {24,6,2,2}*1152c, {6,6,2,2}*1152b, {6,12,2,2}*1152b
   5-fold covers : {6,6,2,10}*1440c, {6,6,10,2}*1440c, {6,30,2,2}*1440a, {30,6,2,2}*1440c
   6-fold covers : {36,6,2,2}*1728b, {12,6,2,2}*1728a, {18,6,2,4}*1728b, {6,6,2,4}*1728c, {18,6,4,2}*1728b, {18,12,2,2}*1728b, {6,6,4,2}*1728c, {6,12,2,2}*1728c, {6,6,2,12}*1728c, {12,6,2,6}*1728b, {12,6,6,2}*1728d, {6,6,2,4}*1728d, {6,6,12,2}*1728e, {6,12,2,2}*1728g, {12,6,2,2}*1728g, {6,6,4,6}*1728c, {6,6,4,2}*1728h, {6,12,2,6}*1728c, {6,12,6,2}*1728f, {6,6,6,4}*1728i
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope