Polytope of Type {2,2,16,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,16,10}*1280
if this polytope has a name.
Group : SmallGroup(1280,1076041)
Rank : 5
Schlafli Type : {2,2,16,10}
Number of vertices, edges, etc : 2, 2, 16, 80, 10
Order of s₀s₁s₂s₃s₄ : 80
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 : {2,2,8,10}*640
   4-fold quotients : {2,2,4,10}*320
   5-fold quotients : {2,2,16,2}*256
   8-fold quotients : {2,2,2,10}*160
   10-fold quotients : {2,2,8,2}*128
   16-fold quotients : {2,2,2,5}*80
   20-fold quotients : {2,2,4,2}*64
   40-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (15,20)(16,21)(17,22)(18,23)(19,24)(25,35)(26,36)(27,37)(28,38)(29,39)
(30,40)(31,41)(32,42)(33,43)(34,44)(45,65)(46,66)(47,67)(48,68)(49,69)(50,70)
(51,71)(52,72)(53,73)(54,74)(55,80)(56,81)(57,82)(58,83)(59,84)(60,75)(61,76)
(62,77)(63,78)(64,79);;
s3 := ( 5,45)( 6,49)( 7,48)( 8,47)( 9,46)(10,50)(11,54)(12,53)(13,52)(14,51)
(15,60)(16,64)(17,63)(18,62)(19,61)(20,55)(21,59)(22,58)(23,57)(24,56)(25,75)
(26,79)(27,78)(28,77)(29,76)(30,80)(31,84)(32,83)(33,82)(34,81)(35,65)(36,69)
(37,68)(38,67)(39,66)(40,70)(41,74)(42,73)(43,72)(44,71);;
s4 := ( 5, 6)( 7, 9)(10,11)(12,14)(15,16)(17,19)(20,21)(22,24)(25,26)(27,29)
(30,31)(32,34)(35,36)(37,39)(40,41)(42,44)(45,46)(47,49)(50,51)(52,54)(55,56)
(57,59)(60,61)(62,64)(65,66)(67,69)(70,71)(72,74)(75,76)(77,79)(80,81)
(82,84);;
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*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(84)!(1,2);
s1 := Sym(84)!(3,4);
s2 := Sym(84)!(15,20)(16,21)(17,22)(18,23)(19,24)(25,35)(26,36)(27,37)(28,38)
(29,39)(30,40)(31,41)(32,42)(33,43)(34,44)(45,65)(46,66)(47,67)(48,68)(49,69)
(50,70)(51,71)(52,72)(53,73)(54,74)(55,80)(56,81)(57,82)(58,83)(59,84)(60,75)
(61,76)(62,77)(63,78)(64,79);
s3 := Sym(84)!( 5,45)( 6,49)( 7,48)( 8,47)( 9,46)(10,50)(11,54)(12,53)(13,52)
(14,51)(15,60)(16,64)(17,63)(18,62)(19,61)(20,55)(21,59)(22,58)(23,57)(24,56)
(25,75)(26,79)(27,78)(28,77)(29,76)(30,80)(31,84)(32,83)(33,82)(34,81)(35,65)
(36,69)(37,68)(38,67)(39,66)(40,70)(41,74)(42,73)(43,72)(44,71);
s4 := Sym(84)!( 5, 6)( 7, 9)(10,11)(12,14)(15,16)(17,19)(20,21)(22,24)(25,26)
(27,29)(30,31)(32,34)(35,36)(37,39)(40,41)(42,44)(45,46)(47,49)(50,51)(52,54)
(55,56)(57,59)(60,61)(62,64)(65,66)(67,69)(70,71)(72,74)(75,76)(77,79)(80,81)
(82,84);
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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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*s2*s3*s2*s3*s2*s3 >;

to this polytope