Polytope of Type {8,80}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,80}*1280a
if this polytope has a name.
Group : SmallGroup(1280,82962)
Rank : 3
Schlafli Type : {8,80}
Number of vertices, edges, etc : 8, 320, 80
Order of s₀s₁s₂ : 80
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {8,40}*640d
   4-fold quotients : {4,40}*320b, {8,20}*320a
   5-fold quotients : {8,16}*256a
   8-fold quotients : {4,20}*160, {8,10}*160
   10-fold quotients : {8,8}*128c
   16-fold quotients : {2,20}*80, {4,10}*80
   20-fold quotients : {8,4}*64a, {4,8}*64b
   32-fold quotients : {2,10}*40
   40-fold quotients : {4,4}*32, {8,2}*32
   64-fold quotients : {2,5}*20
   80-fold quotients : {2,4}*16, {4,2}*16
   160-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*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*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*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*s0*s1*s2*s1 >;

References : None.
to this polytope