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Polytope of Type {10,6,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,6,2,6}*1440
if this polytope has a name.
Group : SmallGroup(1440,5924)
Rank : 5
Schlafli Type : {10,6,2,6}
Number of vertices, edges, etc : 10, 30, 6, 6, 6
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 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 : {10,6,2,3}*720
   3-fold quotients : {10,2,2,6}*480, {10,6,2,2}*480
   5-fold quotients : {2,6,2,6}*288
   6-fold quotients : {5,2,2,6}*240, {10,2,2,3}*240
   9-fold quotients : {10,2,2,2}*160
   10-fold quotients : {2,3,2,6}*144, {2,6,2,3}*144
   12-fold quotients : {5,2,2,3}*120
   15-fold quotients : {2,2,2,6}*96, {2,6,2,2}*96
   18-fold quotients : {5,2,2,2}*80
   20-fold quotients : {2,3,2,3}*72
   30-fold quotients : {2,2,2,3}*48, {2,3,2,2}*48
   45-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 6)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)
(27,28)(29,30);;
s1 := ( 1, 5)( 2, 9)( 3,13)( 4,11)( 6,15)( 7,19)( 8,17)(10,21)(12,25)(14,23)
(18,29)(20,27)(24,26)(28,30);;
s2 := ( 1, 7)( 2, 3)( 4, 8)( 5,17)( 6,18)( 9,11)(10,12)(13,19)(14,20)(15,27)
(16,28)(21,23)(22,24)(25,29)(26,30);;
s3 := (33,34)(35,36);;
s4 := (31,35)(32,33)(34,36);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(36)!( 5, 6)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26)(27,28)(29,30);
s1 := Sym(36)!( 1, 5)( 2, 9)( 3,13)( 4,11)( 6,15)( 7,19)( 8,17)(10,21)(12,25)
(14,23)(18,29)(20,27)(24,26)(28,30);
s2 := Sym(36)!( 1, 7)( 2, 3)( 4, 8)( 5,17)( 6,18)( 9,11)(10,12)(13,19)(14,20)
(15,27)(16,28)(21,23)(22,24)(25,29)(26,30);
s3 := Sym(36)!(33,34)(35,36);
s4 := Sym(36)!(31,35)(32,33)(34,36);
poly := sub<Sym(36)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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