Polytope of Type {12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240800)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 80, 480, 80
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 20
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
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 : {6,12}*960a, {12,6}*960a
   4-fold quotients : {6,6}*480
   8-fold quotients : {6,6}*240a, {6,6}*240b, {6,6}*240c
   16-fold quotients : {6,6}*120
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 7,32)( 8,31)( 9,36)(10,35)(13,39)(14,40)(15,34)(16,33)(17,37)
(18,38)(19,29)(20,30)(21,23)(22,24)(25,43)(26,44)(27,28)(41,42)(47,48)(49,50)
(51,75)(52,76)(53,79)(54,80)(55,56)(57,84)(58,83)(59,77)(60,78)(61,82)(62,81)
(63,74)(64,73)(65,68)(66,67)(69,88)(70,87);;
s1 := ( 1, 3)( 2, 4)( 5,11)( 6,12)( 7,18)( 8,17)( 9,25)(10,26)(13,21)(14,22)
(15,27)(16,28)(19,20)(23,31)(24,32)(29,42)(30,41)(35,37)(36,38)(39,44)(40,43)
(45,47)(46,48)(49,56)(50,55)(51,61)(52,62)(53,70)(54,69)(57,66)(58,65)(59,72)
(60,71)(67,76)(68,75)(73,85)(74,86)(77,78)(79,82)(80,81)(83,87)(84,88);;
s2 := ( 1,45)( 2,46)( 3,48)( 4,47)( 5,71)( 6,72)( 7,51)( 8,52)( 9,73)(10,74)
(11,85)(12,86)(13,88)(14,87)(15,66)(16,65)(17,61)(18,62)(19,79)(20,80)(21,60)
(22,59)(23,78)(24,77)(25,83)(26,84)(27,49)(28,50)(29,53)(30,54)(31,76)(32,75)
(33,68)(34,67)(35,63)(36,64)(37,82)(38,81)(39,69)(40,70)(41,55)(42,56)(43,58)
(44,57);;
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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(88)!( 3, 4)( 7,32)( 8,31)( 9,36)(10,35)(13,39)(14,40)(15,34)(16,33)
(17,37)(18,38)(19,29)(20,30)(21,23)(22,24)(25,43)(26,44)(27,28)(41,42)(47,48)
(49,50)(51,75)(52,76)(53,79)(54,80)(55,56)(57,84)(58,83)(59,77)(60,78)(61,82)
(62,81)(63,74)(64,73)(65,68)(66,67)(69,88)(70,87);
s1 := Sym(88)!( 1, 3)( 2, 4)( 5,11)( 6,12)( 7,18)( 8,17)( 9,25)(10,26)(13,21)
(14,22)(15,27)(16,28)(19,20)(23,31)(24,32)(29,42)(30,41)(35,37)(36,38)(39,44)
(40,43)(45,47)(46,48)(49,56)(50,55)(51,61)(52,62)(53,70)(54,69)(57,66)(58,65)
(59,72)(60,71)(67,76)(68,75)(73,85)(74,86)(77,78)(79,82)(80,81)(83,87)(84,88);
s2 := Sym(88)!( 1,45)( 2,46)( 3,48)( 4,47)( 5,71)( 6,72)( 7,51)( 8,52)( 9,73)
(10,74)(11,85)(12,86)(13,88)(14,87)(15,66)(16,65)(17,61)(18,62)(19,79)(20,80)
(21,60)(22,59)(23,78)(24,77)(25,83)(26,84)(27,49)(28,50)(29,53)(30,54)(31,76)
(32,75)(33,68)(34,67)(35,63)(36,64)(37,82)(38,81)(39,69)(40,70)(41,55)(42,56)
(43,58)(44,57);
poly := sub<Sym(88)|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*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
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