Polytope of Type {4,2,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,18}*288
if this polytope has a name.
Group : SmallGroup(288,356)
Rank : 4
Schlafli Type : {4,2,18}
Number of vertices, edges, etc : 4, 4, 18, 18
Order of s₀s₁s₂s₃ : 36
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,18,2} of size 576
   {4,2,18,4} of size 1152
   {4,2,18,4} of size 1152
   {4,2,18,4} of size 1152
   {4,2,18,6} of size 1728
   {4,2,18,6} of size 1728
Vertex Figure Of :
   {2,4,2,18} of size 576
   {3,4,2,18} of size 864
   {4,4,2,18} of size 1152
   {6,4,2,18} of size 1728
   {3,4,2,18} of size 1728
   {6,4,2,18} of size 1728
   {6,4,2,18} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,9}*144, {2,2,18}*144
   3-fold quotients : {4,2,6}*96
   4-fold quotients : {2,2,9}*72
   6-fold quotients : {4,2,3}*48, {2,2,6}*48
   9-fold quotients : {4,2,2}*32
   12-fold quotients : {2,2,3}*24
   18-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,36}*576, {4,4,18}*576, {8,2,18}*576
   3-fold covers : {4,2,54}*864, {12,2,18}*864, {4,6,18}*864a, {4,6,18}*864b
   4-fold covers : {4,4,36}*1152, {4,8,18}*1152a, {8,4,18}*1152a, {4,8,18}*1152b, {8,4,18}*1152b, {4,4,18}*1152a, {8,2,36}*1152, {4,2,72}*1152, {16,2,18}*1152, {4,4,18}*1152d
   5-fold covers : {20,2,18}*1440, {4,10,18}*1440, {4,2,90}*1440
   6-fold covers : {4,2,108}*1728, {4,4,54}*1728, {8,2,54}*1728, {12,2,36}*1728, {4,6,36}*1728a, {4,12,18}*1728a, {12,4,18}*1728, {24,2,18}*1728, {8,6,18}*1728a, {4,6,36}*1728b, {8,6,18}*1728b, {4,12,18}*1728b
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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