Polytope of Type {3,2,30,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,30,2}*720
if this polytope has a name.
Group : SmallGroup(720,831)
Rank : 5
Schlafli Type : {3,2,30,2}
Number of vertices, edges, etc : 3, 3, 30, 30, 2
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,30,2,2} of size 1440
Vertex Figure Of :
   {2,3,2,30,2} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,15,2}*360
   3-fold quotients : {3,2,10,2}*240
   5-fold quotients : {3,2,6,2}*144
   6-fold quotients : {3,2,5,2}*120
   10-fold quotients : {3,2,3,2}*72
   15-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,60,2}*1440, {3,2,30,4}*1440a, {6,2,30,2}*1440
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 6, 7)( 8, 9)(10,11)(12,13)(14,17)(15,16)(18,19)(20,23)(21,22)(24,25)
(26,29)(27,28)(30,33)(31,32);;
s3 := ( 4,20)( 5,14)( 6,12)( 7,22)( 8,10)( 9,30)(11,16)(13,26)(15,24)(17,32)
(18,21)(19,31)(23,28)(25,27)(29,33);;
s4 := (34,35);;
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, 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(35)!(2,3);
s1 := Sym(35)!(1,2);
s2 := Sym(35)!( 6, 7)( 8, 9)(10,11)(12,13)(14,17)(15,16)(18,19)(20,23)(21,22)
(24,25)(26,29)(27,28)(30,33)(31,32);
s3 := Sym(35)!( 4,20)( 5,14)( 6,12)( 7,22)( 8,10)( 9,30)(11,16)(13,26)(15,24)
(17,32)(18,21)(19,31)(23,28)(25,27)(29,33);
s4 := Sym(35)!(34,35);
poly := sub<Sym(35)|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, 
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 >;

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