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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,20}*1920
if this polytope has a name.
Group : SmallGroup(1920,151308)
Rank : 5
Schlafli Type : {3,2,4,20}
Number of vertices, edges, etc : 3, 3, 8, 80, 40
Order of s₀s₁s₂s₃s₄ : 60
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 : {3,2,4,20}*960
   4-fold quotients : {3,2,2,20}*480, {3,2,4,10}*480
   5-fold quotients : {3,2,4,4}*384
   8-fold quotients : {3,2,2,10}*240
   10-fold quotients : {3,2,4,4}*192
   16-fold quotients : {3,2,2,5}*120
   20-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96
   40-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := (24,29)(25,30)(26,31)(27,32)(28,33)(34,39)(35,40)(36,41)(37,42)(38,43)
(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)(64,79)
(65,80)(66,81)(67,82)(68,83)(69,74)(70,75)(71,76)(72,77)(73,78);;
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)(24,64)
(25,68)(26,67)(27,66)(28,65)(29,69)(30,73)(31,72)(32,71)(33,70)(34,74)(35,78)
(36,77)(37,76)(38,75)(39,79)(40,83)(41,82)(42,81)(43,80);;
s4 := ( 4, 5)( 6, 8)( 9,10)(11,13)(14,20)(15,19)(16,23)(17,22)(18,21)(24,25)
(26,28)(29,30)(31,33)(34,40)(35,39)(36,43)(37,42)(38,41)(44,65)(45,64)(46,68)
(47,67)(48,66)(49,70)(50,69)(51,73)(52,72)(53,71)(54,80)(55,79)(56,83)(57,82)
(58,81)(59,75)(60,74)(61,78)(62,77)(63,76);;
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, 
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*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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)!(24,29)(25,30)(26,31)(27,32)(28,33)(34,39)(35,40)(36,41)(37,42)
(38,43)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)
(64,79)(65,80)(66,81)(67,82)(68,83)(69,74)(70,75)(71,76)(72,77)(73,78);
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)
(24,64)(25,68)(26,67)(27,66)(28,65)(29,69)(30,73)(31,72)(32,71)(33,70)(34,74)
(35,78)(36,77)(37,76)(38,75)(39,79)(40,83)(41,82)(42,81)(43,80);
s4 := Sym(83)!( 4, 5)( 6, 8)( 9,10)(11,13)(14,20)(15,19)(16,23)(17,22)(18,21)
(24,25)(26,28)(29,30)(31,33)(34,40)(35,39)(36,43)(37,42)(38,41)(44,65)(45,64)
(46,68)(47,67)(48,66)(49,70)(50,69)(51,73)(52,72)(53,71)(54,80)(55,79)(56,83)
(57,82)(58,81)(59,75)(60,74)(61,78)(62,77)(63,76);
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, 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*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope