Polytope of Type {2,6,15,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,15,4}*1440
if this polytope has a name.
Group : SmallGroup(1440,5900)
Rank : 5
Schlafli Type : {2,6,15,4}
Number of vertices, edges, etc : 2, 6, 45, 30, 4
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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 : {2,2,15,4}*480
   5-fold quotients : {2,6,3,4}*288
   15-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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