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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,20,4}*960
if this polytope has a name.
Group : SmallGroup(960,7401)
Rank : 5
Schlafli Type : {3,2,20,4}
Number of vertices, edges, etc : 3, 3, 20, 40, 4
Order of s₀s₁s₂s₃s₄ : 60
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,20,4,2} of size 1920
Vertex Figure Of :
   {2,3,2,20,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,20,2}*480, {3,2,10,4}*480
   4-fold quotients : {3,2,10,2}*240
   5-fold quotients : {3,2,4,4}*192
   8-fold quotients : {3,2,5,2}*120
   10-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96
   20-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,20,8}*1920a, {3,2,40,4}*1920a, {3,2,20,8}*1920b, {3,2,40,4}*1920b, {3,2,20,4}*1920, {6,2,20,4}*1920
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 8)( 6, 7)(10,13)(11,12)(15,18)(16,17)(20,23)(21,22)(24,34)(25,38)
(26,37)(27,36)(28,35)(29,39)(30,43)(31,42)(32,41)(33,40)(45,48)(46,47)(50,53)
(51,52)(55,58)(56,57)(60,63)(61,62)(64,74)(65,78)(66,77)(67,76)(68,75)(69,79)
(70,83)(71,82)(72,81)(73,80);;
s3 := ( 4,25)( 5,24)( 6,28)( 7,27)( 8,26)( 9,30)(10,29)(11,33)(12,32)(13,31)
(14,35)(15,34)(16,38)(17,37)(18,36)(19,40)(20,39)(21,43)(22,42)(23,41)(44,65)
(45,64)(46,68)(47,67)(48,66)(49,70)(50,69)(51,73)(52,72)(53,71)(54,75)(55,74)
(56,78)(57,77)(58,76)(59,80)(60,79)(61,83)(62,82)(63,81);;
s4 := ( 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)(21,61)(22,62)(23,63)(24,69)
(25,70)(26,71)(27,72)(28,73)(29,64)(30,65)(31,66)(32,67)(33,68)(34,79)(35,80)
(36,81)(37,82)(38,83)(39,74)(40,75)(41,76)(42,77)(43,78);;
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*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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(83)!(2,3);
s1 := Sym(83)!(1,2);
s2 := Sym(83)!( 5, 8)( 6, 7)(10,13)(11,12)(15,18)(16,17)(20,23)(21,22)(24,34)
(25,38)(26,37)(27,36)(28,35)(29,39)(30,43)(31,42)(32,41)(33,40)(45,48)(46,47)
(50,53)(51,52)(55,58)(56,57)(60,63)(61,62)(64,74)(65,78)(66,77)(67,76)(68,75)
(69,79)(70,83)(71,82)(72,81)(73,80);
s3 := Sym(83)!( 4,25)( 5,24)( 6,28)( 7,27)( 8,26)( 9,30)(10,29)(11,33)(12,32)
(13,31)(14,35)(15,34)(16,38)(17,37)(18,36)(19,40)(20,39)(21,43)(22,42)(23,41)
(44,65)(45,64)(46,68)(47,67)(48,66)(49,70)(50,69)(51,73)(52,72)(53,71)(54,75)
(55,74)(56,78)(57,77)(58,76)(59,80)(60,79)(61,83)(62,82)(63,81);
s4 := Sym(83)!( 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)(21,61)(22,62)(23,63)
(24,69)(25,70)(26,71)(27,72)(28,73)(29,64)(30,65)(31,66)(32,67)(33,68)(34,79)
(35,80)(36,81)(37,82)(38,83)(39,74)(40,75)(41,76)(42,77)(43,78);
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*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope