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Polytope of Type {2,30,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,6}*1080
if this polytope has a name.
Group : SmallGroup(1080,337)
Rank : 4
Schlafli Type : {2,30,6}
Number of vertices, edges, etc : 2, 45, 135, 9
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) :
   5-fold quotients : {2,6,6}*216
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6,15)( 7,17)( 8,16)( 9,12)(10,14)(11,13)(18,33)(19,35)(20,34)
(21,45)(22,47)(23,46)(24,42)(25,44)(26,43)(27,39)(28,41)(29,40)(30,36)(31,38)
(32,37);;
s2 := ( 3,21)( 4,22)( 5,23)( 6,18)( 7,19)( 8,20)( 9,30)(10,31)(11,32)(12,27)
(13,28)(14,29)(15,24)(16,25)(17,26)(33,36)(34,37)(35,38)(39,45)(40,46)
(41,47);;
s3 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(18,19)(21,22)(24,25)(27,28)(30,31)
(33,35)(36,38)(39,41)(42,44)(45,47);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(47)!(1,2);
s1 := Sym(47)!( 4, 5)( 6,15)( 7,17)( 8,16)( 9,12)(10,14)(11,13)(18,33)(19,35)
(20,34)(21,45)(22,47)(23,46)(24,42)(25,44)(26,43)(27,39)(28,41)(29,40)(30,36)
(31,38)(32,37);
s2 := Sym(47)!( 3,21)( 4,22)( 5,23)( 6,18)( 7,19)( 8,20)( 9,30)(10,31)(11,32)
(12,27)(13,28)(14,29)(15,24)(16,25)(17,26)(33,36)(34,37)(35,38)(39,45)(40,46)
(41,47);
s3 := Sym(47)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(18,19)(21,22)(24,25)(27,28)
(30,31)(33,35)(36,38)(39,41)(42,44)(45,47);
poly := sub<Sym(47)|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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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