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Polytope of Type {2,6,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,30}*1080
if this polytope has a name.
Group : SmallGroup(1080,337)
Rank : 4
Schlafli Type : {2,6,30}
Number of vertices, edges, etc : 2, 9, 135, 45
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)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)(31,32)
(34,35)(37,38)(40,41)(43,44)(46,47);;
s2 := ( 6,15)( 7,16)( 8,17)( 9,12)(10,13)(11,14)(18,35)(19,33)(20,34)(21,47)
(22,45)(23,46)(24,44)(25,42)(26,43)(27,41)(28,39)(29,40)(30,38)(31,36)
(32,37);;
s3 := ( 3,21)( 4,23)( 5,22)( 6,18)( 7,20)( 8,19)( 9,30)(10,32)(11,31)(12,27)
(13,29)(14,28)(15,24)(16,26)(17,25)(33,36)(34,38)(35,37)(39,45)(40,47)(41,46)
(43,44);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*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(47)!(1,2);
s1 := Sym(47)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23)(25,26)(28,29)
(31,32)(34,35)(37,38)(40,41)(43,44)(46,47);
s2 := Sym(47)!( 6,15)( 7,16)( 8,17)( 9,12)(10,13)(11,14)(18,35)(19,33)(20,34)
(21,47)(22,45)(23,46)(24,44)(25,42)(26,43)(27,41)(28,39)(29,40)(30,38)(31,36)
(32,37);
s3 := Sym(47)!( 3,21)( 4,23)( 5,22)( 6,18)( 7,20)( 8,19)( 9,30)(10,32)(11,31)
(12,27)(13,29)(14,28)(15,24)(16,26)(17,25)(33,36)(34,38)(35,37)(39,45)(40,47)
(41,46)(43,44);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*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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