Polytope of Type {3,2,4,9,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,9,2}*864
if this polytope has a name.
Group : SmallGroup(864,3999)
Rank : 6
Schlafli Type : {3,2,4,9,2}
Number of vertices, edges, etc : 3, 3, 4, 18, 9, 2
Order of s₀s₁s₂s₃s₄s₅ : 18
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,4,9,2,2} of size 1728
Vertex Figure Of :
   {2,3,2,4,9,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,2,4,3,2}*288
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,4,9,2}*1728, {3,2,4,18,2}*1728b, {3,2,4,18,2}*1728c, {6,2,4,9,2}*1728
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5,10)( 6,12)( 7,14)( 8,16)(11,21)(13,23)(17,27)(24,33)(26,35)(28,36)
(30,37)(32,38);;
s3 := ( 4, 5)( 6, 9)( 7, 8)(10,18)(11,17)(12,19)(13,15)(14,16)(20,26)(21,27)
(22,24)(23,25)(28,34)(29,35)(30,32)(31,33)(36,39)(37,38);;
s4 := ( 4, 9)( 5, 7)( 6,17)( 8,13)(10,14)(11,26)(12,27)(15,22)(16,23)(18,19)
(20,34)(21,35)(24,30)(25,31)(28,32)(29,39)(33,37)(36,38);;
s5 := (40,41);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, 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);
s1 := Sym(41)!(1,2);
s2 := Sym(41)!( 5,10)( 6,12)( 7,14)( 8,16)(11,21)(13,23)(17,27)(24,33)(26,35)
(28,36)(30,37)(32,38);
s3 := Sym(41)!( 4, 5)( 6, 9)( 7, 8)(10,18)(11,17)(12,19)(13,15)(14,16)(20,26)
(21,27)(22,24)(23,25)(28,34)(29,35)(30,32)(31,33)(36,39)(37,38);
s4 := Sym(41)!( 4, 9)( 5, 7)( 6,17)( 8,13)(10,14)(11,26)(12,27)(15,22)(16,23)
(18,19)(20,34)(21,35)(24,30)(25,31)(28,32)(29,39)(33,37)(36,38);
s5 := Sym(41)!(40,41);
poly := sub<Sym(41)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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