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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,10,16}*1280
if this polytope has a name.
Group : SmallGroup(1280,1076041)
Rank : 5
Schlafli Type : {2,2,10,16}
Number of vertices, edges, etc : 2, 2, 10, 80, 16
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 : {2,2,10,8}*640
   4-fold quotients : {2,2,10,4}*320
   5-fold quotients : {2,2,2,16}*256
   8-fold quotients : {2,2,10,2}*160
   10-fold quotients : {2,2,2,8}*128
   16-fold quotients : {2,2,5,2}*80
   20-fold quotients : {2,2,2,4}*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 := ( 6, 9)( 7, 8)(11,14)(12,13)(16,19)(17,18)(21,24)(22,23)(26,29)(27,28)
(31,34)(32,33)(36,39)(37,38)(41,44)(42,43)(46,49)(47,48)(51,54)(52,53)(56,59)
(57,58)(61,64)(62,63)(66,69)(67,68)(71,74)(72,73)(76,79)(77,78)(81,84)
(82,83);;
s3 := ( 5, 6)( 7, 9)(10,11)(12,14)(15,21)(16,20)(17,24)(18,23)(19,22)(25,36)
(26,35)(27,39)(28,38)(29,37)(30,41)(31,40)(32,44)(33,43)(34,42)(45,66)(46,65)
(47,69)(48,68)(49,67)(50,71)(51,70)(52,74)(53,73)(54,72)(55,81)(56,80)(57,84)
(58,83)(59,82)(60,76)(61,75)(62,79)(63,78)(64,77);;
s4 := ( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)(14,54)
(15,60)(16,61)(17,62)(18,63)(19,64)(20,55)(21,56)(22,57)(23,58)(24,59)(25,75)
(26,76)(27,77)(28,78)(29,79)(30,80)(31,81)(32,82)(33,83)(34,84)(35,65)(36,66)
(37,67)(38,68)(39,69)(40,70)(41,71)(42,72)(43,73)(44,74);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope