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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,20,4}*1280
if this polytope has a name.
Group : SmallGroup(1280,1036282)
Rank : 5
Schlafli Type : {2,2,20,4}
Number of vertices, edges, etc : 2, 2, 40, 80, 8
Order of s₀s₁s₂s₃s₄ : 20
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 : {2,2,20,4}*640
   4-fold quotients : {2,2,20,2}*320, {2,2,10,4}*320
   5-fold quotients : {2,2,4,4}*256
   8-fold quotients : {2,2,10,2}*160
   10-fold quotients : {2,2,4,4}*128
   16-fold quotients : {2,2,5,2}*80
   20-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
   40-fold quotients : {2,2,2,2}*32
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)(15,20)(16,24)(17,23)(18,22)(19,21)(26,29)
(27,28)(31,34)(32,33)(35,40)(36,44)(37,43)(38,42)(39,41)(45,65)(46,69)(47,68)
(48,67)(49,66)(50,70)(51,74)(52,73)(53,72)(54,71)(55,80)(56,84)(57,83)(58,82)
(59,81)(60,75)(61,79)(62,78)(63,77)(64,76);;
s3 := ( 5,46)( 6,45)( 7,49)( 8,48)( 9,47)(10,51)(11,50)(12,54)(13,53)(14,52)
(15,56)(16,55)(17,59)(18,58)(19,57)(20,61)(21,60)(22,64)(23,63)(24,62)(25,66)
(26,65)(27,69)(28,68)(29,67)(30,71)(31,70)(32,74)(33,73)(34,72)(35,76)(36,75)
(37,79)(38,78)(39,77)(40,81)(41,80)(42,84)(43,83)(44,82);;
s4 := (25,30)(26,31)(27,32)(28,33)(29,34)(35,40)(36,41)(37,42)(38,43)(39,44)
(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)(54,64)(65,80)
(66,81)(67,82)(68,83)(69,84)(70,75)(71,76)(72,77)(73,78)(74,79);;
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*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, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s4*s3*s4*s3*s2*s3*s2*s4*s3*s4*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*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(84)!(1,2);
s1 := Sym(84)!(3,4);
s2 := Sym(84)!( 6, 9)( 7, 8)(11,14)(12,13)(15,20)(16,24)(17,23)(18,22)(19,21)
(26,29)(27,28)(31,34)(32,33)(35,40)(36,44)(37,43)(38,42)(39,41)(45,65)(46,69)
(47,68)(48,67)(49,66)(50,70)(51,74)(52,73)(53,72)(54,71)(55,80)(56,84)(57,83)
(58,82)(59,81)(60,75)(61,79)(62,78)(63,77)(64,76);
s3 := Sym(84)!( 5,46)( 6,45)( 7,49)( 8,48)( 9,47)(10,51)(11,50)(12,54)(13,53)
(14,52)(15,56)(16,55)(17,59)(18,58)(19,57)(20,61)(21,60)(22,64)(23,63)(24,62)
(25,66)(26,65)(27,69)(28,68)(29,67)(30,71)(31,70)(32,74)(33,73)(34,72)(35,76)
(36,75)(37,79)(38,78)(39,77)(40,81)(41,80)(42,84)(43,83)(44,82);
s4 := Sym(84)!(25,30)(26,31)(27,32)(28,33)(29,34)(35,40)(36,41)(37,42)(38,43)
(39,44)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)(54,64)
(65,80)(66,81)(67,82)(68,83)(69,84)(70,75)(71,76)(72,77)(73,78)(74,79);
poly := sub<Sym(84)|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*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, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s4*s3*s4*s3*s2*s3*s2*s4*s3*s4*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*s2*s3*s2*s3 >;

to this polytope