Polytope of Type {82,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {82,2,5}*1640
if this polytope has a name.
Group : SmallGroup(1640,64)
Rank : 4
Schlafli Type : {82,2,5}
Number of vertices, edges, etc : 82, 82, 5, 5
Order of s₀s₁s₂s₃ : 410
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 : {41,2,5}*820
   41-fold quotients : {2,2,5}*40
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2,41)( 3,40)( 4,39)( 5,38)( 6,37)( 7,36)( 8,35)( 9,34)(10,33)(11,32)
(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(43,82)
(44,81)(45,80)(46,79)(47,78)(48,77)(49,76)(50,75)(51,74)(52,73)(53,72)(54,71)
(55,70)(56,69)(57,68)(58,67)(59,66)(60,65)(61,64)(62,63);;
s1 := ( 1,43)( 2,42)( 3,82)( 4,81)( 5,80)( 6,79)( 7,78)( 8,77)( 9,76)(10,75)
(11,74)(12,73)(13,72)(14,71)(15,70)(16,69)(17,68)(18,67)(19,66)(20,65)(21,64)
(22,63)(23,62)(24,61)(25,60)(26,59)(27,58)(28,57)(29,56)(30,55)(31,54)(32,53)
(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(41,44);;
s2 := (84,85)(86,87);;
s3 := (83,84)(85,86);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(87)!( 2,41)( 3,40)( 4,39)( 5,38)( 6,37)( 7,36)( 8,35)( 9,34)(10,33)
(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)
(43,82)(44,81)(45,80)(46,79)(47,78)(48,77)(49,76)(50,75)(51,74)(52,73)(53,72)
(54,71)(55,70)(56,69)(57,68)(58,67)(59,66)(60,65)(61,64)(62,63);
s1 := Sym(87)!( 1,43)( 2,42)( 3,82)( 4,81)( 5,80)( 6,79)( 7,78)( 8,77)( 9,76)
(10,75)(11,74)(12,73)(13,72)(14,71)(15,70)(16,69)(17,68)(18,67)(19,66)(20,65)
(21,64)(22,63)(23,62)(24,61)(25,60)(26,59)(27,58)(28,57)(29,56)(30,55)(31,54)
(32,53)(33,52)(34,51)(35,50)(36,49)(37,48)(38,47)(39,46)(40,45)(41,44);
s2 := Sym(87)!(84,85)(86,87);
s3 := Sym(87)!(83,84)(85,86);
poly := sub<Sym(87)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope