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Polytope of Type {20,4,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,4,2,3}*960
if this polytope has a name.
Group : SmallGroup(960,7401)
Rank : 5
Schlafli Type : {20,4,2,3}
Number of vertices, edges, etc : 20, 40, 4, 3, 3
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {20,4,2,3,2} of size 1920
Vertex Figure Of :
   {2,20,4,2,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,2,2,3}*480, {10,4,2,3}*480
   4-fold quotients : {10,2,2,3}*240
   5-fold quotients : {4,4,2,3}*192
   8-fold quotients : {5,2,2,3}*120
   10-fold quotients : {2,4,2,3}*96, {4,2,2,3}*96
   20-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {20,8,2,3}*1920a, {40,4,2,3}*1920a, {20,8,2,3}*1920b, {40,4,2,3}*1920b, {20,4,2,3}*1920, {20,4,2,6}*1920
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(21,31)(22,35)
(23,34)(24,33)(25,32)(26,36)(27,40)(28,39)(29,38)(30,37)(42,45)(43,44)(47,50)
(48,49)(52,55)(53,54)(57,60)(58,59)(61,71)(62,75)(63,74)(64,73)(65,72)(66,76)
(67,80)(68,79)(69,78)(70,77);;
s1 := ( 1,22)( 2,21)( 3,25)( 4,24)( 5,23)( 6,27)( 7,26)( 8,30)( 9,29)(10,28)
(11,32)(12,31)(13,35)(14,34)(15,33)(16,37)(17,36)(18,40)(19,39)(20,38)(41,62)
(42,61)(43,65)(44,64)(45,63)(46,67)(47,66)(48,70)(49,69)(50,68)(51,72)(52,71)
(53,75)(54,74)(55,73)(56,77)(57,76)(58,80)(59,79)(60,78);;
s2 := ( 1,41)( 2,42)( 3,43)( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)
(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,66)
(22,67)(23,68)(24,69)(25,70)(26,61)(27,62)(28,63)(29,64)(30,65)(31,76)(32,77)
(33,78)(34,79)(35,80)(36,71)(37,72)(38,73)(39,74)(40,75);;
s3 := (82,83);;
s4 := (81,82);;
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, 
s3*s4*s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(83)!( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(21,31)
(22,35)(23,34)(24,33)(25,32)(26,36)(27,40)(28,39)(29,38)(30,37)(42,45)(43,44)
(47,50)(48,49)(52,55)(53,54)(57,60)(58,59)(61,71)(62,75)(63,74)(64,73)(65,72)
(66,76)(67,80)(68,79)(69,78)(70,77);
s1 := Sym(83)!( 1,22)( 2,21)( 3,25)( 4,24)( 5,23)( 6,27)( 7,26)( 8,30)( 9,29)
(10,28)(11,32)(12,31)(13,35)(14,34)(15,33)(16,37)(17,36)(18,40)(19,39)(20,38)
(41,62)(42,61)(43,65)(44,64)(45,63)(46,67)(47,66)(48,70)(49,69)(50,68)(51,72)
(52,71)(53,75)(54,74)(55,73)(56,77)(57,76)(58,80)(59,79)(60,78);
s2 := Sym(83)!( 1,41)( 2,42)( 3,43)( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)
(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)
(21,66)(22,67)(23,68)(24,69)(25,70)(26,61)(27,62)(28,63)(29,64)(30,65)(31,76)
(32,77)(33,78)(34,79)(35,80)(36,71)(37,72)(38,73)(39,74)(40,75);
s3 := Sym(83)!(82,83);
s4 := Sym(83)!(81,82);
poly := sub<Sym(83)|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, s3*s4*s3*s4*s3*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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