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Polytope of Type {13,2,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {13,2,30}*1560
if this polytope has a name.
Group : SmallGroup(1560,206)
Rank : 4
Schlafli Type : {13,2,30}
Number of vertices, edges, etc : 13, 13, 30, 30
Order of s0s1s2s3 : 390
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   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) :
   2-fold quotients : {13,2,15}*780
   3-fold quotients : {13,2,10}*520
   5-fold quotients : {13,2,6}*312
   6-fold quotients : {13,2,5}*260
   10-fold quotients : {13,2,3}*156
   15-fold quotients : {13,2,2}*104
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);;
s2 := (16,17)(18,19)(20,21)(22,23)(24,27)(25,26)(28,29)(30,33)(31,32)(34,35)
(36,39)(37,38)(40,43)(41,42);;
s3 := (14,30)(15,24)(16,22)(17,32)(18,20)(19,40)(21,26)(23,36)(25,34)(27,42)
(28,31)(29,41)(33,38)(35,37)(39,43);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*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(43)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);
s1 := Sym(43)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(43)!(16,17)(18,19)(20,21)(22,23)(24,27)(25,26)(28,29)(30,33)(31,32)
(34,35)(36,39)(37,38)(40,43)(41,42);
s3 := Sym(43)!(14,30)(15,24)(16,22)(17,32)(18,20)(19,40)(21,26)(23,36)(25,34)
(27,42)(28,31)(29,41)(33,38)(35,37)(39,43);
poly := sub<Sym(43)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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