Polytope of Type {6,15,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,15,4}*720
if this polytope has a name.
Group : SmallGroup(720,793)
Rank : 4
Schlafli Type : {6,15,4}
Number of vertices, edges, etc : 6, 45, 30, 4
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,15,4,2} of size 1440
Vertex Figure Of :
   {2,6,15,4} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,15,4}*240
   5-fold quotients : {6,3,4}*144
   15-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,15,4}*1440b, {6,30,4}*1440e, {6,30,4}*1440f
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope