Polytope of Type {5,2,4,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,4,18}*1440a
if this polytope has a name.
Group : SmallGroup(1440,1593)
Rank : 5
Schlafli Type : {5,2,4,18}
Number of vertices, edges, etc : 5, 5, 4, 36, 18
Order of s₀s₁s₂s₃s₄ : 180
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,2,18}*720
   3-fold quotients : {5,2,4,6}*480a
   4-fold quotients : {5,2,2,9}*360
   6-fold quotients : {5,2,2,6}*240
   9-fold quotients : {5,2,4,2}*160
   12-fold quotients : {5,2,2,3}*120
   18-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(31,40)(32,41);;
s3 := ( 6,24)( 7,26)( 8,25)( 9,31)(10,30)(11,32)(12,28)(13,27)(14,29)(15,33)
(16,35)(17,34)(18,40)(19,39)(20,41)(21,37)(22,36)(23,38);;
s4 := ( 6, 9)( 7,11)( 8,10)(12,13)(15,18)(16,20)(17,19)(21,22)(24,27)(25,29)
(26,28)(30,31)(33,36)(34,38)(35,37)(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*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*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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(41)!(2,3)(4,5);
s1 := Sym(41)!(1,2)(3,4);
s2 := Sym(41)!(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(31,40)(32,41);
s3 := Sym(41)!( 6,24)( 7,26)( 8,25)( 9,31)(10,30)(11,32)(12,28)(13,27)(14,29)
(15,33)(16,35)(17,34)(18,40)(19,39)(20,41)(21,37)(22,36)(23,38);
s4 := Sym(41)!( 6, 9)( 7,11)( 8,10)(12,13)(15,18)(16,20)(17,19)(21,22)(24,27)
(25,29)(26,28)(30,31)(33,36)(34,38)(35,37)(39,40);
poly := sub<Sym(41)|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*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*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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