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Polytope of Type {3,2,4,10,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,10,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,208118)
Rank : 6
Schlafli Type : {3,2,4,10,4}
Number of vertices, edges, etc : 3, 3, 4, 20, 20, 4
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 : {3,2,2,10,4}*960, {3,2,4,10,2}*960
   4-fold quotients : {3,2,2,10,2}*480
   5-fold quotients : {3,2,4,2,4}*384
   8-fold quotients : {3,2,2,5,2}*240
   10-fold quotients : {3,2,2,2,4}*192, {3,2,4,2,2}*192
   20-fold quotients : {3,2,2,2,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := (44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)
(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82)(73,83);;
s3 := ( 4,44)( 5,48)( 6,47)( 7,46)( 8,45)( 9,49)(10,53)(11,52)(12,51)(13,50)
(14,54)(15,58)(16,57)(17,56)(18,55)(19,59)(20,63)(21,62)(22,61)(23,60)(24,74)
(25,78)(26,77)(27,76)(28,75)(29,79)(30,83)(31,82)(32,81)(33,80)(34,64)(35,68)
(36,67)(37,66)(38,65)(39,69)(40,73)(41,72)(42,71)(43,70);;
s4 := ( 4, 5)( 6, 8)( 9,10)(11,13)(14,15)(16,18)(19,20)(21,23)(24,40)(25,39)
(26,43)(27,42)(28,41)(29,35)(30,34)(31,38)(32,37)(33,36)(44,45)(46,48)(49,50)
(51,53)(54,55)(56,58)(59,60)(61,63)(64,80)(65,79)(66,83)(67,82)(68,81)(69,75)
(70,74)(71,78)(72,77)(73,76);;
s5 := ( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,33)
(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(21,41)(22,42)(23,43)(44,74)
(45,75)(46,76)(47,77)(48,78)(49,79)(50,80)(51,81)(52,82)(53,83)(54,64)(55,65)
(56,66)(57,67)(58,68)(59,69)(60,70)(61,71)(62,72)(63,73);;
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*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, s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(83)!(2,3);
s1 := Sym(83)!(1,2);
s2 := Sym(83)!(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)
(53,63)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82)(73,83);
s3 := Sym(83)!( 4,44)( 5,48)( 6,47)( 7,46)( 8,45)( 9,49)(10,53)(11,52)(12,51)
(13,50)(14,54)(15,58)(16,57)(17,56)(18,55)(19,59)(20,63)(21,62)(22,61)(23,60)
(24,74)(25,78)(26,77)(27,76)(28,75)(29,79)(30,83)(31,82)(32,81)(33,80)(34,64)
(35,68)(36,67)(37,66)(38,65)(39,69)(40,73)(41,72)(42,71)(43,70);
s4 := Sym(83)!( 4, 5)( 6, 8)( 9,10)(11,13)(14,15)(16,18)(19,20)(21,23)(24,40)
(25,39)(26,43)(27,42)(28,41)(29,35)(30,34)(31,38)(32,37)(33,36)(44,45)(46,48)
(49,50)(51,53)(54,55)(56,58)(59,60)(61,63)(64,80)(65,79)(66,83)(67,82)(68,81)
(69,75)(70,74)(71,78)(72,77)(73,76);
s5 := Sym(83)!( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)
(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(21,41)(22,42)(23,43)
(44,74)(45,75)(46,76)(47,77)(48,78)(49,79)(50,80)(51,81)(52,82)(53,83)(54,64)
(55,65)(56,66)(57,67)(58,68)(59,69)(60,70)(61,71)(62,72)(63,73);
poly := sub<Sym(83)|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*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, 
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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