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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,16,2}*1280
if this polytope has a name.
Group : SmallGroup(1280,1076041)
Rank : 5
Schlafli Type : {2,10,16,2}
Number of vertices, edges, etc : 2, 10, 80, 16, 2
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 : {2,10,8,2}*640
   4-fold quotients : {2,10,4,2}*320
   5-fold quotients : {2,2,16,2}*256
   8-fold quotients : {2,10,2,2}*160
   10-fold quotients : {2,2,8,2}*128
   16-fold quotients : {2,5,2,2}*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 := ( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)(25,26)
(29,32)(30,31)(34,37)(35,36)(39,42)(40,41)(44,47)(45,46)(49,52)(50,51)(54,57)
(55,56)(59,62)(60,61)(64,67)(65,66)(69,72)(70,71)(74,77)(75,76)(79,82)
(80,81);;
s2 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,19)(14,18)(15,22)(16,21)(17,20)(23,34)
(24,33)(25,37)(26,36)(27,35)(28,39)(29,38)(30,42)(31,41)(32,40)(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)
(13,58)(14,59)(15,60)(16,61)(17,62)(18,53)(19,54)(20,55)(21,56)(22,57)(23,73)
(24,74)(25,75)(26,76)(27,77)(28,78)(29,79)(30,80)(31,81)(32,82)(33,63)(34,64)
(35,65)(36,66)(37,67)(38,68)(39,69)(40,70)(41,71)(42,72);;
s4 := (83,84);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, 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, 
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)!( 4, 7)( 5, 6)( 9,12)(10,11)(14,17)(15,16)(19,22)(20,21)(24,27)
(25,26)(29,32)(30,31)(34,37)(35,36)(39,42)(40,41)(44,47)(45,46)(49,52)(50,51)
(54,57)(55,56)(59,62)(60,61)(64,67)(65,66)(69,72)(70,71)(74,77)(75,76)(79,82)
(80,81);
s2 := Sym(84)!( 3, 4)( 5, 7)( 8, 9)(10,12)(13,19)(14,18)(15,22)(16,21)(17,20)
(23,34)(24,33)(25,37)(26,36)(27,35)(28,39)(29,38)(30,42)(31,41)(32,40)(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(84)!( 3,43)( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)
(12,52)(13,58)(14,59)(15,60)(16,61)(17,62)(18,53)(19,54)(20,55)(21,56)(22,57)
(23,73)(24,74)(25,75)(26,76)(27,77)(28,78)(29,79)(30,80)(31,81)(32,82)(33,63)
(34,64)(35,65)(36,66)(37,67)(38,68)(39,69)(40,70)(41,71)(42,72);
s4 := Sym(84)!(83,84);
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
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, 
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