Polytope of Type {18,2,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,2,20}*1440
if this polytope has a name.
Group : SmallGroup(1440,1584)
Rank : 4
Schlafli Type : {18,2,20}
Number of vertices, edges, etc : 18, 18, 20, 20
Order of s₀s₁s₂s₃ : 180
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 : {9,2,20}*720, {18,2,10}*720
   3-fold quotients : {6,2,20}*480
   4-fold quotients : {9,2,10}*360, {18,2,5}*360
   5-fold quotients : {18,2,4}*288
   6-fold quotients : {3,2,20}*240, {6,2,10}*240
   8-fold quotients : {9,2,5}*180
   9-fold quotients : {2,2,20}*160
   10-fold quotients : {9,2,4}*144, {18,2,2}*144
   12-fold quotients : {3,2,10}*120, {6,2,5}*120
   15-fold quotients : {6,2,4}*96
   18-fold quotients : {2,2,10}*80
   20-fold quotients : {9,2,2}*72
   24-fold quotients : {3,2,5}*60
   30-fold quotients : {3,2,4}*48, {6,2,2}*48
   36-fold quotients : {2,2,5}*40
   45-fold quotients : {2,2,4}*32
   60-fold quotients : {3,2,2}*24
   90-fold quotients : {2,2,2}*16
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 := (20,21)(22,23)(25,28)(26,27)(29,30)(31,32)(33,36)(34,35)(37,38);;
s3 := (19,25)(20,22)(21,31)(23,33)(24,27)(26,29)(28,37)(30,34)(32,35)(36,38);;
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*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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