Polytope of Type {4,30,2}

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

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

Permutation Representation (Magma) :

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

to this polytope