Polytope of Type {10,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,6,3}*1440
if this polytope has a name.
Group : SmallGroup(1440,5871)
Rank : 4
Schlafli Type : {10,6,3}
Number of vertices, edges, etc : 10, 120, 36, 12
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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) :
   3-fold quotients : {10,6,3}*480
   4-fold quotients : {10,6,3}*360
   5-fold quotients : {2,6,3}*288
   12-fold quotients : {10,2,3}*120
   15-fold quotients : {2,6,3}*96
   20-fold quotients : {2,6,3}*72
   24-fold quotients : {5,2,3}*60
   30-fold quotients : {2,3,3}*48
   60-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope