Polytope of Type {2,18,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,18,4,2}*576a
if this polytope has a name.
Group : SmallGroup(576,5012)
Rank : 5
Schlafli Type : {2,18,4,2}
Number of vertices, edges, etc : 2, 18, 36, 4, 2
Order of s₀s₁s₂s₃s₄ : 36
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,18,4,2,2} of size 1152
   {2,18,4,2,3} of size 1728
Vertex Figure Of :
   {2,2,18,4,2} of size 1152
   {3,2,18,4,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,18,2,2}*288
   3-fold quotients : {2,6,4,2}*192a
   4-fold quotients : {2,9,2,2}*144
   6-fold quotients : {2,6,2,2}*96
   9-fold quotients : {2,2,4,2}*64
   12-fold quotients : {2,3,2,2}*48
   18-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,18,4,4}*1152, {2,36,4,2}*1152a, {4,18,4,2}*1152a, {2,18,8,2}*1152
   3-fold covers : {2,54,4,2}*1728a, {2,18,12,2}*1728a, {2,18,4,6}*1728, {6,18,4,2}*1728a, {6,18,4,2}*1728b, {2,18,12,2}*1728b
Permutation Representation (GAP) :

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