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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,20,2,2}*1280a
if this polytope has a name.
Group : SmallGroup(1280,1035863)
Rank : 5
Schlafli Type : {8,20,2,2}
Number of vertices, edges, etc : 8, 80, 20, 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 : {4,20,2,2}*640, {8,10,2,2}*640
   4-fold quotients : {2,20,2,2}*320, {4,10,2,2}*320
   5-fold quotients : {8,4,2,2}*256a
   8-fold quotients : {2,10,2,2}*160
   10-fold quotients : {4,4,2,2}*128, {8,2,2,2}*128
   16-fold quotients : {2,5,2,2}*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 := (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);;
s1 := ( 1,41)( 2,45)( 3,44)( 4,43)( 5,42)( 6,46)( 7,50)( 8,49)( 9,48)(10,47)
(11,56)(12,60)(13,59)(14,58)(15,57)(16,51)(17,55)(18,54)(19,53)(20,52)(21,61)
(22,65)(23,64)(24,63)(25,62)(26,66)(27,70)(28,69)(29,68)(30,67)(31,76)(32,80)
(33,79)(34,78)(35,77)(36,71)(37,75)(38,74)(39,73)(40,72);;
s2 := ( 1, 2)( 3, 5)( 6, 7)( 8,10)(11,12)(13,15)(16,17)(18,20)(21,22)(23,25)
(26,27)(28,30)(31,32)(33,35)(36,37)(38,40)(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);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope