Polytope of Type {6,2,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,30}*720
if this polytope has a name.
Group : SmallGroup(720,831)
Rank : 4
Schlafli Type : {6,2,30}
Number of vertices, edges, etc : 6, 6, 30, 30
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,2,30,2} of size 1440
Vertex Figure Of :
   {2,6,2,30} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,30}*360, {6,2,15}*360
   3-fold quotients : {6,2,10}*240, {2,2,30}*240
   4-fold quotients : {3,2,15}*180
   5-fold quotients : {6,2,6}*144
   6-fold quotients : {3,2,10}*120, {6,2,5}*120, {2,2,15}*120
   9-fold quotients : {2,2,10}*80
   10-fold quotients : {3,2,6}*72, {6,2,3}*72
   12-fold quotients : {3,2,5}*60
   15-fold quotients : {2,2,6}*48, {6,2,2}*48
   18-fold quotients : {2,2,5}*40
   20-fold quotients : {3,2,3}*36
   30-fold quotients : {2,2,3}*24, {3,2,2}*24
   45-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,2,30}*1440, {6,2,60}*1440, {6,4,30}*1440
Permutation Representation (GAP) :

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