Polytope of Type {2,4,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,40}*1280b
if this polytope has a name.
Group : SmallGroup(1280,323570)
Rank : 4
Schlafli Type : {2,4,40}
Number of vertices, edges, etc : 2, 8, 160, 80
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 : {2,4,20}*640
   4-fold quotients : {2,4,20}*320
   5-fold quotients : {2,4,8}*256b
   8-fold quotients : {2,2,20}*160, {2,4,10}*160
   10-fold quotients : {2,4,4}*128
   16-fold quotients : {2,2,10}*80
   20-fold quotients : {2,4,4}*64
   32-fold quotients : {2,2,5}*40
   40-fold quotients : {2,2,4}*32, {2,4,2}*32
   80-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope