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Polytope of Type {4,18,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,18,2}*288a
if this polytope has a name.
Group : SmallGroup(288,356)
Rank : 4
Schlafli Type : {4,18,2}
Number of vertices, edges, etc : 4, 36, 18, 2
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,18,2,2} of size 576
   {4,18,2,3} of size 864
   {4,18,2,4} of size 1152
   {4,18,2,5} of size 1440
   {4,18,2,6} of size 1728
Vertex Figure Of :
   {2,4,18,2} of size 576
   {4,4,18,2} of size 1152
   {6,4,18,2} of size 1728
   {3,4,18,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,18,2}*144
   3-fold quotients : {4,6,2}*96a
   4-fold quotients : {2,9,2}*72
   6-fold quotients : {2,6,2}*48
   9-fold quotients : {4,2,2}*32
   12-fold quotients : {2,3,2}*24
   18-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,36,2}*576a, {4,18,4}*576a, {8,18,2}*576
   3-fold covers : {4,54,2}*864a, {12,18,2}*864a, {4,18,6}*864a, {4,18,6}*864b, {12,18,2}*864b
   4-fold covers : {4,36,4}*1152a, {8,36,2}*1152a, {4,72,2}*1152a, {8,36,2}*1152b, {4,72,2}*1152b, {4,36,2}*1152a, {4,18,8}*1152a, {8,18,4}*1152a, {16,18,2}*1152, {4,18,4}*1152a, {4,18,2}*1152b
   5-fold covers : {20,18,2}*1440a, {4,18,10}*1440a, {4,90,2}*1440a
   6-fold covers : {4,108,2}*1728a, {4,54,4}*1728a, {8,54,2}*1728, {4,18,12}*1728a, {12,18,4}*1728a, {4,36,6}*1728a, {4,36,6}*1728b, {24,18,2}*1728a, {8,18,6}*1728a, {8,18,6}*1728b, {12,36,2}*1728a, {12,36,2}*1728b, {24,18,2}*1728b, {4,18,12}*1728b, {12,18,4}*1728b
Permutation Representation (GAP) :
s0 := (19,28)(20,29)(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36);;
s1 := ( 1,19)( 2,21)( 3,20)( 4,26)( 5,25)( 6,27)( 7,23)( 8,22)( 9,24)(10,28)
(11,30)(12,29)(13,35)(14,34)(15,36)(16,32)(17,31)(18,33);;
s2 := ( 1, 4)( 2, 6)( 3, 5)( 7, 8)(10,13)(11,15)(12,14)(16,17)(19,22)(20,24)
(21,23)(25,26)(28,31)(29,33)(30,32)(34,35);;
s3 := (37,38);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(38)!(19,28)(20,29)(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36);
s1 := Sym(38)!( 1,19)( 2,21)( 3,20)( 4,26)( 5,25)( 6,27)( 7,23)( 8,22)( 9,24)
(10,28)(11,30)(12,29)(13,35)(14,34)(15,36)(16,32)(17,31)(18,33);
s2 := Sym(38)!( 1, 4)( 2, 6)( 3, 5)( 7, 8)(10,13)(11,15)(12,14)(16,17)(19,22)
(20,24)(21,23)(25,26)(28,31)(29,33)(30,32)(34,35);
s3 := Sym(38)!(37,38);
poly := sub<Sym(38)|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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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