Polytope of Type {2,20,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,4}*1280a
if this polytope has a name.
Group : SmallGroup(1280,323570)
Rank : 4
Schlafli Type : {2,20,4}
Number of vertices, edges, etc : 2, 80, 160, 16
Order of s₀s₁s₂s₃ : 40
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 : {2,20,4}*640
   4-fold quotients : {2,20,4}*320
   5-fold quotients : {2,4,4}*256
   8-fold quotients : {2,20,2}*160, {2,10,4}*160
   10-fold quotients : {2,4,4}*128
   16-fold quotients : {2,10,2}*80
   20-fold quotients : {2,4,4}*64
   32-fold quotients : {2,5,2}*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 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(23,38)(24,42)
(25,41)(26,40)(27,39)(28,33)(29,37)(30,36)(31,35)(32,34)(44,47)(45,46)(49,52)
(50,51)(54,57)(55,56)(59,62)(60,61)(63,78)(64,82)(65,81)(66,80)(67,79)(68,73)
(69,77)(70,76)(71,75)(72,74);;
s2 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,19)(14,18)(15,22)(16,21)(17,20)(23,24)
(25,27)(28,29)(30,32)(33,39)(34,38)(35,42)(36,41)(37,40)(43,64)(44,63)(45,67)
(46,66)(47,65)(48,69)(49,68)(50,72)(51,71)(52,70)(53,79)(54,78)(55,82)(56,81)
(57,80)(58,74)(59,73)(60,77)(61,76)(62,75);;
s3 := ( 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);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*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*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope