Polytope of Type {10,12,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,12,3}*1440
if this polytope has a name.
Group : SmallGroup(1440,5871)
Rank : 4
Schlafli Type : {10,12,3}
Number of vertices, edges, etc : 10, 120, 36, 6
Order of s₀s₁s₂s₃ : 30
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 : {10,4,3}*480
   4-fold quotients : {10,6,3}*360
   5-fold quotients : {2,12,3}*288
   12-fold quotients : {10,2,3}*120
   15-fold quotients : {2,4,3}*96
   20-fold quotients : {2,6,3}*72
   24-fold quotients : {5,2,3}*60
   30-fold quotients : {2,4,3}*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, 7)( 2, 8)( 3, 5)( 4, 6)( 9,19)(10,20)(11,17)(12,18)(13,15)(14,16)
(21,47)(22,48)(23,45)(24,46)(25,43)(26,44)(27,41)(28,42)(29,59)(30,60)(31,57)
(32,58)(33,55)(34,56)(35,53)(36,54)(37,51)(38,52)(39,49)(40,50);;
s2 := ( 1,21)( 2,22)( 3,24)( 4,23)( 5,25)( 6,26)( 7,28)( 8,27)( 9,29)(10,30)
(11,32)(12,31)(13,33)(14,34)(15,36)(16,35)(17,37)(18,38)(19,40)(20,39)(43,44)
(47,48)(51,52)(55,56)(59,60);;
s3 := ( 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);;
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, s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*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, 7)( 2, 8)( 3, 5)( 4, 6)( 9,19)(10,20)(11,17)(12,18)(13,15)
(14,16)(21,47)(22,48)(23,45)(24,46)(25,43)(26,44)(27,41)(28,42)(29,59)(30,60)
(31,57)(32,58)(33,55)(34,56)(35,53)(36,54)(37,51)(38,52)(39,49)(40,50);
s2 := Sym(60)!( 1,21)( 2,22)( 3,24)( 4,23)( 5,25)( 6,26)( 7,28)( 8,27)( 9,29)
(10,30)(11,32)(12,31)(13,33)(14,34)(15,36)(16,35)(17,37)(18,38)(19,40)(20,39)
(43,44)(47,48)(51,52)(55,56)(59,60);
s3 := 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);
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, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
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