Polytope of Type {10,2,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2,18}*720
if this polytope has a name.
Group : SmallGroup(720,402)
Rank : 4
Schlafli Type : {10,2,18}
Number of vertices, edges, etc : 10, 10, 18, 18
Order of s₀s₁s₂s₃ : 90
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,2,18,2} of size 1440
Vertex Figure Of :
   {2,10,2,18} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,18}*360, {10,2,9}*360
   3-fold quotients : {10,2,6}*240
   4-fold quotients : {5,2,9}*180
   5-fold quotients : {2,2,18}*144
   6-fold quotients : {5,2,6}*120, {10,2,3}*120
   9-fold quotients : {10,2,2}*80
   10-fold quotients : {2,2,9}*72
   12-fold quotients : {5,2,3}*60
   15-fold quotients : {2,2,6}*48
   18-fold quotients : {5,2,2}*40
   30-fold quotients : {2,2,3}*24
   45-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,2,36}*1440, {20,2,18}*1440, {10,4,18}*1440
Permutation Representation (GAP) :

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

to this polytope