Polytope of Type {2,30,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,6}*720a
if this polytope has a name.
Group : SmallGroup(720,813)
Rank : 4
Schlafli Type : {2,30,6}
Number of vertices, edges, etc : 2, 30, 90, 6
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,30,6,2} of size 1440
Vertex Figure Of :
   {2,2,30,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,10,6}*240
   5-fold quotients : {2,6,6}*144b
   9-fold quotients : {2,10,2}*80
   10-fold quotients : {2,6,3}*72
   15-fold quotients : {2,2,6}*48
   18-fold quotients : {2,5,2}*40
   30-fold quotients : {2,2,3}*24
   45-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,60,6}*1440a, {2,30,12}*1440a, {4,30,6}*1440a
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 7)( 5, 6)( 8,13)( 9,17)(10,16)(11,15)(12,14)(19,22)(20,21)(23,28)
(24,32)(25,31)(26,30)(27,29)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)
(42,44);;
s2 := ( 3, 9)( 4, 8)( 5,12)( 6,11)( 7,10)(13,14)(15,17)(18,39)(19,38)(20,42)
(21,41)(22,40)(23,34)(24,33)(25,37)(26,36)(27,35)(28,44)(29,43)(30,47)(31,46)
(32,45);;
s3 := ( 3,18)( 4,19)( 5,20)( 6,21)( 7,22)( 8,28)( 9,29)(10,30)(11,31)(12,32)
(13,23)(14,24)(15,25)(16,26)(17,27)(38,43)(39,44)(40,45)(41,46)(42,47);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(47)!(1,2);
s1 := Sym(47)!( 4, 7)( 5, 6)( 8,13)( 9,17)(10,16)(11,15)(12,14)(19,22)(20,21)
(23,28)(24,32)(25,31)(26,30)(27,29)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)
(42,44);
s2 := Sym(47)!( 3, 9)( 4, 8)( 5,12)( 6,11)( 7,10)(13,14)(15,17)(18,39)(19,38)
(20,42)(21,41)(22,40)(23,34)(24,33)(25,37)(26,36)(27,35)(28,44)(29,43)(30,47)
(31,46)(32,45);
s3 := Sym(47)!( 3,18)( 4,19)( 5,20)( 6,21)( 7,22)( 8,28)( 9,29)(10,30)(11,31)
(12,32)(13,23)(14,24)(15,25)(16,26)(17,27)(38,43)(39,44)(40,45)(41,46)(42,47);
poly := sub<Sym(47)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope