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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,30,4}*1440a
if this polytope has a name.
Group : SmallGroup(1440,5685)
Rank : 5
Schlafli Type : {3,2,30,4}
Number of vertices, edges, etc : 3, 3, 30, 60, 4
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 : {3,2,30,2}*720
   3-fold quotients : {3,2,10,4}*480
   4-fold quotients : {3,2,15,2}*360
   5-fold quotients : {3,2,6,4}*288a
   6-fold quotients : {3,2,10,2}*240
   10-fold quotients : {3,2,6,2}*144
   12-fold quotients : {3,2,5,2}*120
   15-fold quotients : {3,2,2,4}*96
   20-fold quotients : {3,2,3,2}*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 := ( 5, 8)( 6, 7)( 9,14)(10,18)(11,17)(12,16)(13,15)(20,23)(21,22)(24,29)
(25,33)(26,32)(27,31)(28,30)(35,38)(36,37)(39,44)(40,48)(41,47)(42,46)(43,45)
(50,53)(51,52)(54,59)(55,63)(56,62)(57,61)(58,60);;
s3 := ( 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)(34,55)(35,54)(36,58)(37,57)(38,56)(39,50)(40,49)
(41,53)(42,52)(43,51)(44,60)(45,59)(46,63)(47,62)(48,61);;
s4 := ( 4,34)( 5,35)( 6,36)( 7,37)( 8,38)( 9,39)(10,40)(11,41)(12,42)(13,43)
(14,44)(15,45)(16,46)(17,47)(18,48)(19,49)(20,50)(21,51)(22,52)(23,53)(24,54)
(25,55)(26,56)(27,57)(28,58)(29,59)(30,60)(31,61)(32,62)(33,63);;
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*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope