Polytope of Type {3,6,10}

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

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

References : None.
to this polytope