Polytope of Type {2,3,2,36}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,2,36}*864
if this polytope has a name.
Group : SmallGroup(864,2437)
Rank : 5
Schlafli Type : {2,3,2,36}
Number of vertices, edges, etc : 2, 3, 3, 36, 36
Order of s₀s₁s₂s₃s₄ : 36
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,3,2,36,2} of size 1728
Vertex Figure Of :
   {2,2,3,2,36} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,2,18}*432
   3-fold quotients : {2,3,2,12}*288
   4-fold quotients : {2,3,2,9}*216
   6-fold quotients : {2,3,2,6}*144
   9-fold quotients : {2,3,2,4}*96
   12-fold quotients : {2,3,2,3}*72
   18-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,3,2,72}*1728, {2,6,2,36}*1728
Permutation Representation (GAP) :

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