Polytope of Type {40,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,4,2}*1280b
if this polytope has a name.
Group : SmallGroup(1280,323570)
Rank : 4
Schlafli Type : {40,4,2}
Number of vertices, edges, etc : 80, 160, 8, 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 : {20,4,2}*640
   4-fold quotients : {20,4,2}*320
   5-fold quotients : {8,4,2}*256b
   8-fold quotients : {20,2,2}*160, {10,4,2}*160
   10-fold quotients : {4,4,2}*128
   16-fold quotients : {10,2,2}*80
   20-fold quotients : {4,4,2}*64
   32-fold quotients : {5,2,2}*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)( 2,45)( 3,44)( 4,43)( 5,42)( 6,46)( 7,50)( 8,49)( 9,48)(10,47)
(11,51)(12,55)(13,54)(14,53)(15,52)(16,56)(17,60)(18,59)(19,58)(20,57)(21,76)
(22,80)(23,79)(24,78)(25,77)(26,71)(27,75)(28,74)(29,73)(30,72)(31,66)(32,70)
(33,69)(34,68)(35,67)(36,61)(37,65)(38,64)(39,63)(40,62);;
s1 := ( 1, 2)( 3, 5)( 6, 7)( 8,10)(11,17)(12,16)(13,20)(14,19)(15,18)(21,22)
(23,25)(26,27)(28,30)(31,37)(32,36)(33,40)(34,39)(35,38)(41,62)(42,61)(43,65)
(44,64)(45,63)(46,67)(47,66)(48,70)(49,69)(50,68)(51,77)(52,76)(53,80)(54,79)
(55,78)(56,72)(57,71)(58,75)(59,74)(60,73);;
s2 := ( 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)(21,61)
(22,62)(23,63)(24,64)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)
(33,73)(34,74)(35,75)(36,76)(37,77)(38,78)(39,79)(40,80);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope