Polytope of Type {3,2,12,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,12,10}*1440
if this polytope has a name.
Group : SmallGroup(1440,5282)
Rank : 5
Schlafli Type : {3,2,12,10}
Number of vertices, edges, etc : 3, 3, 12, 60, 10
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 : {3,2,6,10}*720
   3-fold quotients : {3,2,4,10}*480
   5-fold quotients : {3,2,12,2}*288
   6-fold quotients : {3,2,2,10}*240
   10-fold quotients : {3,2,6,2}*144
   12-fold quotients : {3,2,2,5}*120
   15-fold quotients : {3,2,4,2}*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 := ( 9,14)(10,15)(11,16)(12,17)(13,18)(24,29)(25,30)(26,31)(27,32)(28,33)
(34,49)(35,50)(36,51)(37,52)(38,53)(39,59)(40,60)(41,61)(42,62)(43,63)(44,54)
(45,55)(46,56)(47,57)(48,58);;
s3 := ( 4,39)( 5,43)( 6,42)( 7,41)( 8,40)( 9,34)(10,38)(11,37)(12,36)(13,35)
(14,44)(15,48)(16,47)(17,46)(18,45)(19,54)(20,58)(21,57)(22,56)(23,55)(24,49)
(25,53)(26,52)(27,51)(28,50)(29,59)(30,63)(31,62)(32,61)(33,60);;
s4 := ( 4, 5)( 6, 8)( 9,10)(11,13)(14,15)(16,18)(19,20)(21,23)(24,25)(26,28)
(29,30)(31,33)(34,35)(36,38)(39,40)(41,43)(44,45)(46,48)(49,50)(51,53)(54,55)
(56,58)(59,60)(61,63);;
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*s3*s4*s3*s4*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope