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Polytope of Type {2,80,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,80,2}*640
if this polytope has a name.
Group : SmallGroup(640,15814)
Rank : 4
Schlafli Type : {2,80,2}
Number of vertices, edges, etc : 2, 80, 80, 2
Order of s0s1s2s3 : 80
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,80,2,2} of size 1280
   {2,80,2,3} of size 1920
Vertex Figure Of :
   {2,2,80,2} of size 1280
   {3,2,80,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,40,2}*320
   4-fold quotients : {2,20,2}*160
   5-fold quotients : {2,16,2}*128
   8-fold quotients : {2,10,2}*80
   10-fold quotients : {2,8,2}*64
   16-fold quotients : {2,5,2}*40
   20-fold quotients : {2,4,2}*32
   40-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,80,4}*1280a, {4,80,2}*1280a, {2,160,2}*1280
   3-fold covers : {2,240,2}*1920, {2,80,6}*1920, {6,80,2}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 7)( 5, 6)( 9,12)(10,11)(13,18)(14,22)(15,21)(16,20)(17,19)(23,33)
(24,37)(25,36)(26,35)(27,34)(28,38)(29,42)(30,41)(31,40)(32,39)(43,63)(44,67)
(45,66)(46,65)(47,64)(48,68)(49,72)(50,71)(51,70)(52,69)(53,78)(54,82)(55,81)
(56,80)(57,79)(58,73)(59,77)(60,76)(61,75)(62,74);;
s2 := ( 3,44)( 4,43)( 5,47)( 6,46)( 7,45)( 8,49)( 9,48)(10,52)(11,51)(12,50)
(13,59)(14,58)(15,62)(16,61)(17,60)(18,54)(19,53)(20,57)(21,56)(22,55)(23,74)
(24,73)(25,77)(26,76)(27,75)(28,79)(29,78)(30,82)(31,81)(32,80)(33,64)(34,63)
(35,67)(36,66)(37,65)(38,69)(39,68)(40,72)(41,71)(42,70);;
s3 := (83,84);;
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, 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*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*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*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(84)!(1,2);
s1 := Sym(84)!( 4, 7)( 5, 6)( 9,12)(10,11)(13,18)(14,22)(15,21)(16,20)(17,19)
(23,33)(24,37)(25,36)(26,35)(27,34)(28,38)(29,42)(30,41)(31,40)(32,39)(43,63)
(44,67)(45,66)(46,65)(47,64)(48,68)(49,72)(50,71)(51,70)(52,69)(53,78)(54,82)
(55,81)(56,80)(57,79)(58,73)(59,77)(60,76)(61,75)(62,74);
s2 := Sym(84)!( 3,44)( 4,43)( 5,47)( 6,46)( 7,45)( 8,49)( 9,48)(10,52)(11,51)
(12,50)(13,59)(14,58)(15,62)(16,61)(17,60)(18,54)(19,53)(20,57)(21,56)(22,55)
(23,74)(24,73)(25,77)(26,76)(27,75)(28,79)(29,78)(30,82)(31,81)(32,80)(33,64)
(34,63)(35,67)(36,66)(37,65)(38,69)(39,68)(40,72)(41,71)(42,70);
s3 := Sym(84)!(83,84);
poly := sub<Sym(84)|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, 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*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*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*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 >; 
 

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