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

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

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

Permutation Representation (Magma) :

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

to this polytope