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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}*720a
if this polytope has a name.
Group : SmallGroup(720,813)
Rank : 4
Schlafli Type : {2,6,30}
Number of vertices, edges, etc : 2, 6, 90, 30
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,30,2} of size 1440
Vertex Figure Of :
   {2,2,6,30} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,6,10}*240
   5-fold quotients : {2,6,6}*144c
   9-fold quotients : {2,2,10}*80
   10-fold quotients : {2,3,6}*72
   15-fold quotients : {2,6,2}*48
   18-fold quotients : {2,2,5}*40
   30-fold quotients : {2,3,2}*24
   45-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,60}*1440a, {2,12,30}*1440a, {4,6,30}*1440a
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 8,13)( 9,14)(10,15)(11,16)(12,17)(18,33)(19,34)(20,35)(21,36)(22,37)
(23,43)(24,44)(25,45)(26,46)(27,47)(28,38)(29,39)(30,40)(31,41)(32,42);;
s2 := ( 3,23)( 4,27)( 5,26)( 6,25)( 7,24)( 8,18)( 9,22)(10,21)(11,20)(12,19)
(13,28)(14,32)(15,31)(16,30)(17,29)(33,38)(34,42)(35,41)(36,40)(37,39)(44,47)
(45,46);;
s3 := ( 3, 4)( 5, 7)( 8,14)( 9,13)(10,17)(11,16)(12,15)(18,19)(20,22)(23,29)
(24,28)(25,32)(26,31)(27,30)(33,34)(35,37)(38,44)(39,43)(40,47)(41,46)
(42,45);;
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*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(47)!(1,2);
s1 := Sym(47)!( 8,13)( 9,14)(10,15)(11,16)(12,17)(18,33)(19,34)(20,35)(21,36)
(22,37)(23,43)(24,44)(25,45)(26,46)(27,47)(28,38)(29,39)(30,40)(31,41)(32,42);
s2 := Sym(47)!( 3,23)( 4,27)( 5,26)( 6,25)( 7,24)( 8,18)( 9,22)(10,21)(11,20)
(12,19)(13,28)(14,32)(15,31)(16,30)(17,29)(33,38)(34,42)(35,41)(36,40)(37,39)
(44,47)(45,46);
s3 := Sym(47)!( 3, 4)( 5, 7)( 8,14)( 9,13)(10,17)(11,16)(12,15)(18,19)(20,22)
(23,29)(24,28)(25,32)(26,31)(27,30)(33,34)(35,37)(38,44)(39,43)(40,47)(41,46)
(42,45);
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*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2 >; 
 

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