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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,10,12}*1440
if this polytope has a name.
Group : SmallGroup(1440,5282)
Rank : 5
Schlafli Type : {3,2,10,12}
Number of vertices, edges, etc : 3, 3, 10, 60, 12
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 : {3,2,10,6}*720
   3-fold quotients : {3,2,10,4}*480
   5-fold quotients : {3,2,2,12}*288
   6-fold quotients : {3,2,10,2}*240
   10-fold quotients : {3,2,2,6}*144
   12-fold quotients : {3,2,5,2}*120
   15-fold quotients : {3,2,2,4}*96
   20-fold quotients : {3,2,2,3}*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 := ( 5, 8)( 6, 7)(10,13)(11,12)(15,18)(16,17)(20,23)(21,22)(25,28)(26,27)
(30,33)(31,32)(35,38)(36,37)(40,43)(41,42)(45,48)(46,47)(50,53)(51,52)(55,58)
(56,57)(60,63)(61,62);;
s3 := ( 4, 5)( 6, 8)( 9,15)(10,14)(11,18)(12,17)(13,16)(19,20)(21,23)(24,30)
(25,29)(26,33)(27,32)(28,31)(34,50)(35,49)(36,53)(37,52)(38,51)(39,60)(40,59)
(41,63)(42,62)(43,61)(44,55)(45,54)(46,58)(47,57)(48,56);;
s4 := ( 4,39)( 5,40)( 6,41)( 7,42)( 8,43)( 9,34)(10,35)(11,36)(12,37)(13,38)
(14,44)(15,45)(16,46)(17,47)(18,48)(19,54)(20,55)(21,56)(22,57)(23,58)(24,49)
(25,50)(26,51)(27,52)(28,53)(29,59)(30,60)(31,61)(32,62)(33,63);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope