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Polytope of Type {2,2,10,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,10,4,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,236178)
Rank : 6
Schlafli Type : {2,2,10,4,6}
Number of vertices, edges, etc : 2, 2, 10, 20, 12, 6
Order of s0s1s2s3s4s5 : 60
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {2,2,10,2,6}*960
   3-fold quotients : {2,2,10,4,2}*640
   4-fold quotients : {2,2,5,2,6}*480, {2,2,10,2,3}*480
   5-fold quotients : {2,2,2,4,6}*384a
   6-fold quotients : {2,2,10,2,2}*320
   8-fold quotients : {2,2,5,2,3}*240
   10-fold quotients : {2,2,2,2,6}*192
   12-fold quotients : {2,2,5,2,2}*160
   15-fold quotients : {2,2,2,4,2}*128
   20-fold quotients : {2,2,2,2,3}*96
   30-fold quotients : {2,2,2,2,2}*64
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 9)( 7, 8)(11,14)(12,13)(16,19)(17,18)(21,24)(22,23)(26,29)(27,28)
(31,34)(32,33)(36,39)(37,38)(41,44)(42,43)(46,49)(47,48)(51,54)(52,53)(56,59)
(57,58)(61,64)(62,63);;
s3 := ( 5, 6)( 7, 9)(10,11)(12,14)(15,16)(17,19)(20,21)(22,24)(25,26)(27,29)
(30,31)(32,34)(35,51)(36,50)(37,54)(38,53)(39,52)(40,56)(41,55)(42,59)(43,58)
(44,57)(45,61)(46,60)(47,64)(48,63)(49,62);;
s4 := ( 5,35)( 6,36)( 7,37)( 8,38)( 9,39)(10,45)(11,46)(12,47)(13,48)(14,49)
(15,40)(16,41)(17,42)(18,43)(19,44)(20,50)(21,51)(22,52)(23,53)(24,54)(25,60)
(26,61)(27,62)(28,63)(29,64)(30,55)(31,56)(32,57)(33,58)(34,59);;
s5 := ( 5,10)( 6,11)( 7,12)( 8,13)( 9,14)(20,25)(21,26)(22,27)(23,28)(24,29)
(35,40)(36,41)(37,42)(38,43)(39,44)(50,55)(51,56)(52,57)(53,58)(54,59);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
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(64)!(1,2);
s1 := Sym(64)!(3,4);
s2 := Sym(64)!( 6, 9)( 7, 8)(11,14)(12,13)(16,19)(17,18)(21,24)(22,23)(26,29)
(27,28)(31,34)(32,33)(36,39)(37,38)(41,44)(42,43)(46,49)(47,48)(51,54)(52,53)
(56,59)(57,58)(61,64)(62,63);
s3 := Sym(64)!( 5, 6)( 7, 9)(10,11)(12,14)(15,16)(17,19)(20,21)(22,24)(25,26)
(27,29)(30,31)(32,34)(35,51)(36,50)(37,54)(38,53)(39,52)(40,56)(41,55)(42,59)
(43,58)(44,57)(45,61)(46,60)(47,64)(48,63)(49,62);
s4 := Sym(64)!( 5,35)( 6,36)( 7,37)( 8,38)( 9,39)(10,45)(11,46)(12,47)(13,48)
(14,49)(15,40)(16,41)(17,42)(18,43)(19,44)(20,50)(21,51)(22,52)(23,53)(24,54)
(25,60)(26,61)(27,62)(28,63)(29,64)(30,55)(31,56)(32,57)(33,58)(34,59);
s5 := Sym(64)!( 5,10)( 6,11)( 7,12)( 8,13)( 9,14)(20,25)(21,26)(22,27)(23,28)
(24,29)(35,40)(36,41)(37,42)(38,43)(39,44)(50,55)(51,56)(52,57)(53,58)(54,59);
poly := sub<Sym(64)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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