Polytope of Type {9,2,36}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,36}*1296
if this polytope has a name.
Group : SmallGroup(1296,798)
Rank : 4
Schlafli Type : {9,2,36}
Number of vertices, edges, etc : 9, 9, 36, 36
Order of s₀s₁s₂s₃ : 36
Order of s₀s₁s₂s₃s₂s₁ : 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 : {9,2,18}*648
   3-fold quotients : {3,2,36}*432, {9,2,12}*432
   4-fold quotients : {9,2,9}*324
   6-fold quotients : {3,2,18}*216, {9,2,6}*216
   9-fold quotients : {9,2,4}*144, {3,2,12}*144
   12-fold quotients : {3,2,9}*108, {9,2,3}*108
   18-fold quotients : {9,2,2}*72, {3,2,6}*72
   27-fold quotients : {3,2,4}*48
   36-fold quotients : {3,2,3}*36
   54-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (11,12)(13,14)(16,19)(17,18)(20,21)(22,23)(24,27)(25,26)(28,29)(30,31)
(32,35)(33,34)(36,37)(38,39)(40,43)(41,42)(44,45);;
s3 := (10,16)(11,13)(12,22)(14,24)(15,18)(17,20)(19,30)(21,32)(23,26)(25,28)
(27,38)(29,40)(31,34)(33,36)(35,44)(37,41)(39,42)(43,45);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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(45)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(45)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(45)!(11,12)(13,14)(16,19)(17,18)(20,21)(22,23)(24,27)(25,26)(28,29)
(30,31)(32,35)(33,34)(36,37)(38,39)(40,43)(41,42)(44,45);
s3 := Sym(45)!(10,16)(11,13)(12,22)(14,24)(15,18)(17,20)(19,30)(21,32)(23,26)
(25,28)(27,38)(29,40)(31,34)(33,36)(35,44)(37,41)(39,42)(43,45);
poly := sub<Sym(45)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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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