Polytope of Type {18,2,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,2,10,2}*1440
if this polytope has a name.
Group : SmallGroup(1440,4583)
Rank : 5
Schlafli Type : {18,2,10,2}
Number of vertices, edges, etc : 18, 18, 10, 10, 2
Order of s₀s₁s₂s₃s₄ : 90
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 : {9,2,10,2}*720, {18,2,5,2}*720
   3-fold quotients : {6,2,10,2}*480
   4-fold quotients : {9,2,5,2}*360
   5-fold quotients : {18,2,2,2}*288
   6-fold quotients : {3,2,10,2}*240, {6,2,5,2}*240
   9-fold quotients : {2,2,10,2}*160
   10-fold quotients : {9,2,2,2}*144
   12-fold quotients : {3,2,5,2}*120
   15-fold quotients : {6,2,2,2}*96
   18-fold quotients : {2,2,5,2}*80
   30-fold quotients : {3,2,2,2}*48
   45-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,18);;
s2 := (21,22)(23,24)(25,26)(27,28);;
s3 := (19,23)(20,21)(22,27)(24,25)(26,28);;
s4 := (29,30);;
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, 
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(30)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);
s1 := Sym(30)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,18);
s2 := Sym(30)!(21,22)(23,24)(25,26)(27,28);
s3 := Sym(30)!(19,23)(20,21)(22,27)(24,25)(26,28);
s4 := Sym(30)!(29,30);
poly := sub<Sym(30)|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, 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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope