Polytope of Type {2,4,30}

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

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

Permutation Representation (Magma) :

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

to this polytope