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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,36,2,2}*1152
if this polytope has a name.
Group : SmallGroup(1152,153172)
Rank : 6
Schlafli Type : {2,2,36,2,2}
Number of vertices, edges, etc : 2, 2, 36, 36, 2, 2
Order of s₀s₁s₂s₃s₄s₅ : 36
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
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 : {2,2,18,2,2}*576
   3-fold quotients : {2,2,12,2,2}*384
   4-fold quotients : {2,2,9,2,2}*288
   6-fold quotients : {2,2,6,2,2}*192
   9-fold quotients : {2,2,4,2,2}*128
   12-fold quotients : {2,2,3,2,2}*96
   18-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(11,14)(12,13)(15,16)(17,18)(19,22)(20,21)(23,24)(25,26)
(27,30)(28,29)(31,32)(33,34)(35,38)(36,37)(39,40);;
s3 := ( 5,11)( 6, 8)( 7,17)( 9,19)(10,13)(12,15)(14,25)(16,27)(18,21)(20,23)
(22,33)(24,35)(26,29)(28,31)(30,39)(32,36)(34,37)(38,40);;
s4 := (41,42);;
s5 := (43,44);;
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*s1*s0*s1, 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, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, 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(44)!(1,2);
s1 := Sym(44)!(3,4);
s2 := Sym(44)!( 6, 7)( 8, 9)(11,14)(12,13)(15,16)(17,18)(19,22)(20,21)(23,24)
(25,26)(27,30)(28,29)(31,32)(33,34)(35,38)(36,37)(39,40);
s3 := Sym(44)!( 5,11)( 6, 8)( 7,17)( 9,19)(10,13)(12,15)(14,25)(16,27)(18,21)
(20,23)(22,33)(24,35)(26,29)(28,31)(30,39)(32,36)(34,37)(38,40);
s4 := Sym(44)!(41,42);
s5 := Sym(44)!(43,44);
poly := sub<Sym(44)|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*s1*s0*s1, 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, 
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
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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