Polytope of Type {4,6,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,30}*1440d
if this polytope has a name.
Group : SmallGroup(1440,5871)
Rank : 4
Schlafli Type : {4,6,30}
Number of vertices, edges, etc : 4, 12, 90, 30
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-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) :
   3-fold quotients : {4,6,10}*480b
   5-fold quotients : {4,6,6}*288e
   10-fold quotients : {4,3,6}*144
   15-fold quotients : {4,6,2}*96c
   30-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope