Polytope of Type {2,12,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,30}*1440d
if this polytope has a name.
Group : SmallGroup(1440,5900)
Rank : 4
Schlafli Type : {2,12,30}
Number of vertices, edges, etc : 2, 12, 180, 30
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {2,4,30}*480c
   5-fold quotients : {2,12,6}*288d
   6-fold quotients : {2,4,15}*240
   15-fold quotients : {2,4,6}*96b
   30-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

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