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

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

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

Permutation Representation (Magma) :

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

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