Polytope of Type {3,2,4,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,30}*1440a
if this polytope has a name.
Group : SmallGroup(1440,5685)
Rank : 5
Schlafli Type : {3,2,4,30}
Number of vertices, edges, etc : 3, 3, 4, 60, 30
Order of s₀s₁s₂s₃s₄ : 60
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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) :
   2-fold quotients : {3,2,2,30}*720
   3-fold quotients : {3,2,4,10}*480
   4-fold quotients : {3,2,2,15}*360
   5-fold quotients : {3,2,4,6}*288a
   6-fold quotients : {3,2,2,10}*240
   10-fold quotients : {3,2,2,6}*144
   12-fold quotients : {3,2,2,5}*120
   15-fold quotients : {3,2,4,2}*96
   20-fold quotients : {3,2,2,3}*72
   30-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := (34,49)(35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)
(44,59)(45,60)(46,61)(47,62)(48,63);;
s3 := ( 4,34)( 5,38)( 6,37)( 7,36)( 8,35)( 9,44)(10,48)(11,47)(12,46)(13,45)
(14,39)(15,43)(16,42)(17,41)(18,40)(19,49)(20,53)(21,52)(22,51)(23,50)(24,59)
(25,63)(26,62)(27,61)(28,60)(29,54)(30,58)(31,57)(32,56)(33,55);;
s4 := ( 4,10)( 5, 9)( 6,13)( 7,12)( 8,11)(14,15)(16,18)(19,25)(20,24)(21,28)
(22,27)(23,26)(29,30)(31,33)(34,40)(35,39)(36,43)(37,42)(38,41)(44,45)(46,48)
(49,55)(50,54)(51,58)(52,57)(53,56)(59,60)(61,63);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(63)!(2,3);
s1 := Sym(63)!(1,2);
s2 := Sym(63)!(34,49)(35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)
(43,58)(44,59)(45,60)(46,61)(47,62)(48,63);
s3 := Sym(63)!( 4,34)( 5,38)( 6,37)( 7,36)( 8,35)( 9,44)(10,48)(11,47)(12,46)
(13,45)(14,39)(15,43)(16,42)(17,41)(18,40)(19,49)(20,53)(21,52)(22,51)(23,50)
(24,59)(25,63)(26,62)(27,61)(28,60)(29,54)(30,58)(31,57)(32,56)(33,55);
s4 := Sym(63)!( 4,10)( 5, 9)( 6,13)( 7,12)( 8,11)(14,15)(16,18)(19,25)(20,24)
(21,28)(22,27)(23,26)(29,30)(31,33)(34,40)(35,39)(36,43)(37,42)(38,41)(44,45)
(46,48)(49,55)(50,54)(51,58)(52,57)(53,56)(59,60)(61,63);
poly := sub<Sym(63)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope