Polytope of Type {2,2,8,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,8,20}*1280a
if this polytope has a name.
Group : SmallGroup(1280,1035863)
Rank : 5
Schlafli Type : {2,2,8,20}
Number of vertices, edges, etc : 2, 2, 8, 80, 20
Order of s₀s₁s₂s₃s₄ : 40
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 : {2,2,4,20}*640, {2,2,8,10}*640
   4-fold quotients : {2,2,2,20}*320, {2,2,4,10}*320
   5-fold quotients : {2,2,8,4}*256a
   8-fold quotients : {2,2,2,10}*160
   10-fold quotients : {2,2,4,4}*128, {2,2,8,2}*128
   16-fold quotients : {2,2,2,5}*80
   20-fold quotients : {2,2,2,4}*64, {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)(35,40)(36,41)(37,42)(38,43)(39,44)
(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)(54,64)(65,75)
(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82)(73,83)(74,84);;
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)(25,65)
(26,69)(27,68)(28,67)(29,66)(30,70)(31,74)(32,73)(33,72)(34,71)(35,80)(36,84)
(37,83)(38,82)(39,81)(40,75)(41,79)(42,78)(43,77)(44,76);;
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)(45,66)(46,65)(47,69)(48,68)(49,67)
(50,71)(51,70)(52,74)(53,73)(54,72)(55,76)(56,75)(57,79)(58,78)(59,77)(60,81)
(61,80)(62,84)(63,83)(64,82);;
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, 
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*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)!(15,20)(16,21)(17,22)(18,23)(19,24)(35,40)(36,41)(37,42)(38,43)
(39,44)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)(54,64)
(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82)(73,83)(74,84);
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)
(25,65)(26,69)(27,68)(28,67)(29,66)(30,70)(31,74)(32,73)(33,72)(34,71)(35,80)
(36,84)(37,83)(38,82)(39,81)(40,75)(41,79)(42,78)(43,77)(44,76);
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)(45,66)(46,65)(47,69)(48,68)
(49,67)(50,71)(51,70)(52,74)(53,73)(54,72)(55,76)(56,75)(57,79)(58,78)(59,77)
(60,81)(61,80)(62,84)(63,83)(64,82);
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, 
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*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope