Polytope of Type {20,2,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,2,18}*1440
if this polytope has a name.
Group : SmallGroup(1440,1584)
Rank : 4
Schlafli Type : {20,2,18}
Number of vertices, edges, etc : 20, 20, 18, 18
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 : {20,2,9}*720, {10,2,18}*720
   3-fold quotients : {20,2,6}*480
   4-fold quotients : {5,2,18}*360, {10,2,9}*360
   5-fold quotients : {4,2,18}*288
   6-fold quotients : {20,2,3}*240, {10,2,6}*240
   8-fold quotients : {5,2,9}*180
   9-fold quotients : {20,2,2}*160
   10-fold quotients : {4,2,9}*144, {2,2,18}*144
   12-fold quotients : {5,2,6}*120, {10,2,3}*120
   15-fold quotients : {4,2,6}*96
   18-fold quotients : {10,2,2}*80
   20-fold quotients : {2,2,9}*72
   24-fold quotients : {5,2,3}*60
   30-fold quotients : {4,2,3}*48, {2,2,6}*48
   36-fold quotients : {5,2,2}*40
   45-fold quotients : {4,2,2}*32
   60-fold quotients : {2,2,3}*24
   90-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope