Polytope of Type {5,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,10}*1600
if this polytope has a name.
Group : SmallGroup(1600,10261)
Rank : 3
Schlafli Type : {5,10}
Number of vertices, edges, etc : 80, 400, 160
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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) :
   5-fold quotients : {5,10}*320b
   10-fold quotients : {5,5}*160
   16-fold quotients : {5,10}*100
   80-fold quotients : {5,2}*20
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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