Polytope of Type {2,2,4,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,9}*288
if this polytope has a name.
Group : SmallGroup(288,835)
Rank : 5
Schlafli Type : {2,2,4,9}
Number of vertices, edges, etc : 2, 2, 4, 18, 9
Order of s₀s₁s₂s₃s₄ : 18
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,4,9,2} of size 576
   {2,2,4,9,4} of size 1152
   {2,2,4,9,6} of size 1728
Vertex Figure Of :
   {2,2,2,4,9} of size 576
   {3,2,2,4,9} of size 864
   {4,2,2,4,9} of size 1152
   {5,2,2,4,9} of size 1440
   {6,2,2,4,9} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,4,3}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,4,9}*576, {2,2,4,9}*576, {2,2,4,18}*576b, {2,2,4,18}*576c
   3-fold covers : {2,2,4,27}*864, {6,2,4,9}*864
   4-fold covers : {2,4,4,9}*1152a, {8,2,4,9}*1152, {2,2,4,36}*1152b, {2,2,4,36}*1152c, {2,4,4,9}*1152b, {4,2,4,9}*1152, {4,2,4,18}*1152b, {4,2,4,18}*1152c, {2,2,8,9}*1152, {2,2,4,18}*1152
   5-fold covers : {10,2,4,9}*1440, {2,2,4,45}*1440
   6-fold covers : {4,2,4,27}*1728, {2,2,4,27}*1728, {2,2,4,54}*1728b, {2,2,4,54}*1728c, {12,2,4,9}*1728, {2,2,12,9}*1728, {2,2,12,18}*1728c, {2,6,4,9}*1728, {6,2,4,9}*1728, {6,2,4,18}*1728b, {6,2,4,18}*1728c
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6,11)( 7,13)( 8,15)( 9,17)(12,22)(14,24)(18,28)(25,34)(27,36)(29,37)
(31,38)(33,39);;
s3 := ( 5, 6)( 7,10)( 8, 9)(11,19)(12,18)(13,20)(14,16)(15,17)(21,27)(22,28)
(23,25)(24,26)(29,35)(30,36)(31,33)(32,34)(37,40)(38,39);;
s4 := ( 5,10)( 6, 8)( 7,18)( 9,14)(11,15)(12,27)(13,28)(16,23)(17,24)(19,20)
(21,35)(22,36)(25,31)(26,32)(29,33)(30,40)(34,38)(37,39);;
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*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(40)!(1,2);
s1 := Sym(40)!(3,4);
s2 := Sym(40)!( 6,11)( 7,13)( 8,15)( 9,17)(12,22)(14,24)(18,28)(25,34)(27,36)
(29,37)(31,38)(33,39);
s3 := Sym(40)!( 5, 6)( 7,10)( 8, 9)(11,19)(12,18)(13,20)(14,16)(15,17)(21,27)
(22,28)(23,25)(24,26)(29,35)(30,36)(31,33)(32,34)(37,40)(38,39);
s4 := Sym(40)!( 5,10)( 6, 8)( 7,18)( 9,14)(11,15)(12,27)(13,28)(16,23)(17,24)
(19,20)(21,35)(22,36)(25,31)(26,32)(29,33)(30,40)(34,38)(37,39);
poly := sub<Sym(40)|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*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope