Polytope of Type {8,20,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,20,2}*1280b
if this polytope has a name.
Group : SmallGroup(1280,323571)
Rank : 4
Schlafli Type : {8,20,2}
Number of vertices, edges, etc : 16, 160, 40, 2
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 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}*640
   4-fold quotients : {4,20,2}*320
   5-fold quotients : {8,4,2}*256b
   8-fold quotients : {2,20,2}*160, {4,10,2}*160
   10-fold quotients : {4,4,2}*128
   16-fold quotients : {2,10,2}*80
   20-fold quotients : {4,4,2}*64
   32-fold quotients : {2,5,2}*40
   40-fold quotients : {2,4,2}*32, {4,2,2}*32
   80-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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