Polytope of Type {2,30,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,4}*1440
if this polytope has a name.
Group : SmallGroup(1440,5890)
Rank : 4
Schlafli Type : {2,30,4}
Number of vertices, edges, etc : 2, 90, 180, 12
Order of s₀s₁s₂s₃ : 20
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) :
   5-fold quotients : {2,6,4}*288
   9-fold quotients : {2,10,4}*160
   10-fold quotients : {2,6,4}*144
   18-fold quotients : {2,10,2}*80
   36-fold quotients : {2,5,2}*40
   45-fold quotients : {2,2,4}*32
   90-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope