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Polytope of Type {12,30,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,30,2}*1440d
if this polytope has a name.
Group : SmallGroup(1440,5900)
Rank : 4
Schlafli Type : {12,30,2}
Number of vertices, edges, etc : 12, 180, 30, 2
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 : {4,30,2}*480c
   5-fold quotients : {12,6,2}*288d
   6-fold quotients : {4,15,2}*240
   15-fold quotients : {4,6,2}*96b
   30-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)
(21,43)(22,44)(23,41)(24,42)(25,47)(26,48)(27,45)(28,46)(29,51)(30,52)(31,49)
(32,50)(33,55)(34,56)(35,53)(36,54)(37,59)(38,60)(39,57)(40,58);;
s1 := ( 1,21)( 2,23)( 3,22)( 4,24)( 5,37)( 6,39)( 7,38)( 8,40)( 9,33)(10,35)
(11,34)(12,36)(13,29)(14,31)(15,30)(16,32)(17,25)(18,27)(19,26)(20,28)(42,43)
(45,57)(46,59)(47,58)(48,60)(49,53)(50,55)(51,54)(52,56);;
s2 := ( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,17)(10,20)(11,19)(12,18)(14,16)(21,25)
(22,28)(23,27)(24,26)(29,37)(30,40)(31,39)(32,38)(34,36)(41,45)(42,48)(43,47)
(44,46)(49,57)(50,60)(51,59)(52,58)(54,56);;
s3 := (61,62);;
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*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(62)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)
(18,20)(21,43)(22,44)(23,41)(24,42)(25,47)(26,48)(27,45)(28,46)(29,51)(30,52)
(31,49)(32,50)(33,55)(34,56)(35,53)(36,54)(37,59)(38,60)(39,57)(40,58);
s1 := Sym(62)!( 1,21)( 2,23)( 3,22)( 4,24)( 5,37)( 6,39)( 7,38)( 8,40)( 9,33)
(10,35)(11,34)(12,36)(13,29)(14,31)(15,30)(16,32)(17,25)(18,27)(19,26)(20,28)
(42,43)(45,57)(46,59)(47,58)(48,60)(49,53)(50,55)(51,54)(52,56);
s2 := Sym(62)!( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,17)(10,20)(11,19)(12,18)(14,16)
(21,25)(22,28)(23,27)(24,26)(29,37)(30,40)(31,39)(32,38)(34,36)(41,45)(42,48)
(43,47)(44,46)(49,57)(50,60)(51,59)(52,58)(54,56);
s3 := Sym(62)!(61,62);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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