Polytope of Type {10,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,5}*1600
if this polytope has a name.
Group : SmallGroup(1600,10261)
Rank : 3
Schlafli Type : {10,5}
Number of vertices, edges, etc : 160, 400, 80
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 : {10,5}*320b
   10-fold quotients : {5,5}*160
   16-fold quotients : {10,5}*100
   80-fold quotients : {2,5}*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)(19,20)(21,22)(25,32)(26,31)
(27,29)(28,30)(35,36)(37,38)(41,48)(42,47)(43,45)(44,46)(51,52)(53,54)(57,64)
(58,63)(59,61)(60,62)(67,68)(69,70)(73,80)(74,79)(75,77)(76,78);;
s1 := ( 2,10)( 3,11)( 5,16)( 6, 7)( 8,13)(14,15)(17,65)(18,74)(19,75)(20,68)
(21,80)(22,71)(23,70)(24,77)(25,73)(26,66)(27,67)(28,76)(29,72)(30,79)(31,78)
(32,69)(33,49)(34,58)(35,59)(36,52)(37,64)(38,55)(39,54)(40,61)(41,57)(42,50)
(43,51)(44,60)(45,56)(46,63)(47,62)(48,53);;
s2 := ( 1,18)( 2,17)( 3,19)( 4,20)( 5,21)( 6,22)( 7,24)( 8,23)( 9,31)(10,32)
(11,30)(12,29)(13,28)(14,27)(15,25)(16,26)(33,66)(34,65)(35,67)(36,68)(37,69)
(38,70)(39,72)(40,71)(41,79)(42,80)(43,78)(44,77)(45,76)(46,75)(47,73)(48,74)
(49,50)(55,56)(57,63)(58,64)(59,62)(60,61);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s1, 
s2*s0*s1*s0*s1*s2*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*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
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