Polytope of Type {9,2,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,30}*1080
if this polytope has a name.
Group : SmallGroup(1080,336)
Rank : 4
Schlafli Type : {9,2,30}
Number of vertices, edges, etc : 9, 9, 30, 30
Order of s₀s₁s₂s₃ : 90
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 : {9,2,15}*540
   3-fold quotients : {9,2,10}*360, {3,2,30}*360
   5-fold quotients : {9,2,6}*216
   6-fold quotients : {9,2,5}*180, {3,2,15}*180
   9-fold quotients : {3,2,10}*120
   10-fold quotients : {9,2,3}*108
   15-fold quotients : {9,2,2}*72, {3,2,6}*72
   18-fold quotients : {3,2,5}*60
   30-fold quotients : {3,2,3}*36
   45-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (12,13)(14,15)(16,17)(18,19)(20,23)(21,22)(24,25)(26,29)(27,28)(30,31)
(32,35)(33,34)(36,39)(37,38);;
s3 := (10,26)(11,20)(12,18)(13,28)(14,16)(15,36)(17,22)(19,32)(21,30)(23,38)
(24,27)(25,37)(29,34)(31,33)(35,39);;
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, 
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*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(39)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(39)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(39)!(12,13)(14,15)(16,17)(18,19)(20,23)(21,22)(24,25)(26,29)(27,28)
(30,31)(32,35)(33,34)(36,39)(37,38);
s3 := Sym(39)!(10,26)(11,20)(12,18)(13,28)(14,16)(15,36)(17,22)(19,32)(21,30)
(23,38)(24,27)(25,37)(29,34)(31,33)(35,39);
poly := sub<Sym(39)|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, 
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope