Polytope of Type {2,2,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,18}*144
if this polytope has a name.
Group : SmallGroup(144,112)
Rank : 4
Schlafli Type : {2,2,18}
Number of vertices, edges, etc : 2, 2, 18, 18
Order of s₀s₁s₂s₃ : 18
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,18,2} of size 288
   {2,2,18,4} of size 576
   {2,2,18,4} of size 576
   {2,2,18,4} of size 576
   {2,2,18,6} of size 864
   {2,2,18,6} of size 864
   {2,2,18,8} of size 1152
   {2,2,18,4} of size 1152
   {2,2,18,9} of size 1296
   {2,2,18,6} of size 1296
   {2,2,18,6} of size 1296
   {2,2,18,3} of size 1296
   {2,2,18,6} of size 1296
   {2,2,18,10} of size 1440
   {2,2,18,12} of size 1728
   {2,2,18,12} of size 1728
   {2,2,18,12} of size 1728
Vertex Figure Of :
   {2,2,2,18} of size 288
   {3,2,2,18} of size 432
   {4,2,2,18} of size 576
   {5,2,2,18} of size 720
   {6,2,2,18} of size 864
   {7,2,2,18} of size 1008
   {8,2,2,18} of size 1152
   {9,2,2,18} of size 1296
   {10,2,2,18} of size 1440
   {11,2,2,18} of size 1584
   {12,2,2,18} of size 1728
   {13,2,2,18} of size 1872
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,9}*72
   3-fold quotients : {2,2,6}*48
   6-fold quotients : {2,2,3}*24
   9-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,36}*288, {2,4,18}*288a, {4,2,18}*288
   3-fold covers : {2,2,54}*432, {2,6,18}*432a, {2,6,18}*432b, {6,2,18}*432
   4-fold covers : {2,4,36}*576a, {4,2,36}*576, {4,4,18}*576, {2,2,72}*576, {2,8,18}*576, {8,2,18}*576, {2,4,18}*576
   5-fold covers : {2,10,18}*720, {10,2,18}*720, {2,2,90}*720
   6-fold covers : {2,2,108}*864, {2,4,54}*864a, {4,2,54}*864, {2,6,36}*864a, {2,6,36}*864b, {6,2,36}*864, {2,12,18}*864a, {12,2,18}*864, {4,6,18}*864a, {6,4,18}*864, {4,6,18}*864b, {2,12,18}*864b
   7-fold covers : {2,14,18}*1008, {14,2,18}*1008, {2,2,126}*1008
   8-fold covers : {4,4,36}*1152, {4,8,18}*1152a, {8,4,18}*1152a, {2,8,36}*1152a, {2,4,72}*1152a, {4,8,18}*1152b, {8,4,18}*1152b, {2,8,36}*1152b, {2,4,72}*1152b, {4,4,18}*1152a, {2,4,36}*1152a, {8,2,36}*1152, {4,2,72}*1152, {2,16,18}*1152, {16,2,18}*1152, {2,2,144}*1152, {2,4,36}*1152b, {4,4,18}*1152d, {2,4,18}*1152b, {2,4,36}*1152c, {2,8,18}*1152b, {2,8,18}*1152c
   9-fold covers : {2,2,162}*1296, {2,18,18}*1296a, {2,18,18}*1296b, {18,2,18}*1296, {6,6,18}*1296a, {2,6,18}*1296a, {2,6,18}*1296b, {2,6,54}*1296a, {2,6,54}*1296b, {6,2,54}*1296, {6,6,18}*1296b, {6,6,18}*1296c, {6,6,18}*1296d, {6,6,18}*1296e, {2,6,18}*1296i
   10-fold covers : {2,10,36}*1440, {10,2,36}*1440, {2,20,18}*1440a, {20,2,18}*1440, {4,10,18}*1440, {10,4,18}*1440, {2,2,180}*1440, {2,4,90}*1440a, {4,2,90}*1440
   11-fold covers : {2,22,18}*1584, {22,2,18}*1584, {2,2,198}*1584
   12-fold covers : {2,4,108}*1728a, {4,2,108}*1728, {4,4,54}*1728, {2,2,216}*1728, {2,8,54}*1728, {8,2,54}*1728, {12,2,36}*1728, {4,6,36}*1728a, {4,12,18}*1728a, {12,4,18}*1728, {6,4,36}*1728, {2,6,72}*1728a, {2,6,72}*1728b, {6,2,72}*1728, {2,24,18}*1728a, {24,2,18}*1728, {6,8,18}*1728, {8,6,18}*1728a, {2,12,36}*1728a, {2,12,36}*1728b, {4,6,36}*1728b, {8,6,18}*1728b, {2,24,18}*1728b, {4,12,18}*1728b, {2,4,54}*1728, {4,6,18}*1728, {6,4,18}*1728a, {6,6,18}*1728, {2,6,18}*1728, {2,6,36}*1728, {6,4,18}*1728b, {2,12,18}*1728a, {2,12,18}*1728b
   13-fold covers : {2,26,18}*1872, {26,2,18}*1872, {2,2,234}*1872
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (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*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*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*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(22)!(1,2);
s1 := Sym(22)!(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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*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*s2*s3 >;

to this polytope