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Polytope of Type {80,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {80,8}*1280a
if this polytope has a name.
Group : SmallGroup(1280,82962)
Rank : 3
Schlafli Type : {80,8}
Number of vertices, edges, etc : 80, 320, 8
Order of s₀s₁s₂ : 80
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {40,8}*640d
   4-fold quotients : {40,4}*320b, {20,8}*320a
   5-fold quotients : {16,8}*256a
   8-fold quotients : {20,4}*160, {10,8}*160
   10-fold quotients : {8,8}*128a
   16-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {4,8}*64a, {8,4}*64b
   32-fold quotients : {10,2}*40
   40-fold quotients : {4,4}*32, {2,8}*32
   64-fold quotients : {5,2}*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 := ( 1,41)( 2,45)( 3,44)( 4,43)( 5,42)( 6,46)( 7,50)( 8,49)( 9,48)(10,47)
(11,56)(12,60)(13,59)(14,58)(15,57)(16,51)(17,55)(18,54)(19,53)(20,52)(21,71)
(22,75)(23,74)(24,73)(25,72)(26,76)(27,80)(28,79)(29,78)(30,77)(31,61)(32,65)
(33,64)(34,63)(35,62)(36,66)(37,70)(38,69)(39,68)(40,67);;
s1 := ( 1, 3)( 4, 5)( 6, 8)( 9,10)(11,18)(12,17)(13,16)(14,20)(15,19)(21,33)
(22,32)(23,31)(24,35)(25,34)(26,38)(27,37)(28,36)(29,40)(30,39)(41,63)(42,62)
(43,61)(44,65)(45,64)(46,68)(47,67)(48,66)(49,70)(50,69)(51,78)(52,77)(53,76)
(54,80)(55,79)(56,73)(57,72)(58,71)(59,75)(60,74);;
s2 := (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);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*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(80)!( 1,41)( 2,45)( 3,44)( 4,43)( 5,42)( 6,46)( 7,50)( 8,49)( 9,48)
(10,47)(11,56)(12,60)(13,59)(14,58)(15,57)(16,51)(17,55)(18,54)(19,53)(20,52)
(21,71)(22,75)(23,74)(24,73)(25,72)(26,76)(27,80)(28,79)(29,78)(30,77)(31,61)
(32,65)(33,64)(34,63)(35,62)(36,66)(37,70)(38,69)(39,68)(40,67);
s1 := Sym(80)!( 1, 3)( 4, 5)( 6, 8)( 9,10)(11,18)(12,17)(13,16)(14,20)(15,19)
(21,33)(22,32)(23,31)(24,35)(25,34)(26,38)(27,37)(28,36)(29,40)(30,39)(41,63)
(42,62)(43,61)(44,65)(45,64)(46,68)(47,67)(48,66)(49,70)(50,69)(51,78)(52,77)
(53,76)(54,80)(55,79)(56,73)(57,72)(58,71)(59,75)(60,74);
s2 := 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);
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
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