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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,2,18}*1152
if this polytope has a name.
Group : SmallGroup(1152,134249)
Rank : 5
Schlafli Type : {4,4,2,18}
Number of vertices, edges, etc : 4, 8, 4, 18, 18
Order of s₀s₁s₂s₃s₄ : 36
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 : {4,4,2,9}*576, {2,4,2,18}*576, {4,2,2,18}*576
   3-fold quotients : {4,4,2,6}*384
   4-fold quotients : {2,4,2,9}*288, {4,2,2,9}*288, {2,2,2,18}*288
   6-fold quotients : {4,4,2,3}*192, {2,4,2,6}*192, {4,2,2,6}*192
   8-fold quotients : {2,2,2,9}*144
   9-fold quotients : {4,4,2,2}*128
   12-fold quotients : {2,4,2,3}*96, {4,2,2,3}*96, {2,2,2,6}*96
   18-fold quotients : {2,4,2,2}*64, {4,2,2,2}*64
   24-fold quotients : {2,2,2,3}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,6);;
s1 := (1,2)(3,5)(4,7)(6,8);;
s2 := (2,4)(3,6);;
s3 := (11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);;
s4 := ( 9,13)(10,11)(12,17)(14,15)(16,21)(18,19)(20,25)(22,23)(24,26);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(26)!(2,3)(4,6);
s1 := Sym(26)!(1,2)(3,5)(4,7)(6,8);
s2 := Sym(26)!(2,4)(3,6);
s3 := Sym(26)!(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26);
s4 := Sym(26)!( 9,13)(10,11)(12,17)(14,15)(16,21)(18,19)(20,25)(22,23)(24,26);
poly := sub<Sym(26)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*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 >;

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