Polytope of Type {20,8,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,8,2,2}*1280a
if this polytope has a name.
Group : SmallGroup(1280,1035863)
Rank : 5
Schlafli Type : {20,8,2,2}
Number of vertices, edges, etc : 20, 80, 8, 2, 2
Order of s₀s₁s₂s₃s₄ : 40
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 : {20,4,2,2}*640, {10,8,2,2}*640
   4-fold quotients : {20,2,2,2}*320, {10,4,2,2}*320
   5-fold quotients : {4,8,2,2}*256a
   8-fold quotients : {10,2,2,2}*160
   10-fold quotients : {4,4,2,2}*128, {2,8,2,2}*128
   16-fold quotients : {5,2,2,2}*80
   20-fold quotients : {2,4,2,2}*64, {4,2,2,2}*64
   40-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope