Polytope of Type {6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*960
if this polytope has a name.
Group : SmallGroup(960,10877)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 80, 240, 80
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,6,2} of size 1920
Vertex Figure Of :
   {2,6,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6}*480
   4-fold quotients : {6,6}*240a, {6,6}*240b, {6,6}*240c
   8-fold quotients : {6,6}*120
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,12}*1920a, {12,6}*1920a
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope