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Polytope of Type {2,4,18}

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