Polytope of Type {6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*384e
if this polytope has a name.
Group : SmallGroup(384,17949)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 32, 96, 32
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,6,2} of size 768
Vertex Figure Of :
   {2,6,6} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,6}*192
   4-fold quotients : {6,6}*96
   8-fold quotients : {3,6}*48, {6,3}*48
   16-fold quotients : {3,3}*24
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,12}*768c, {12,6}*768e, {6,6}*768c, {6,12}*768g, {12,6}*768h
   3-fold covers : {6,6}*1152a, {6,6}*1152e
   5-fold covers : {30,6}*1920a, {6,30}*1920c
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(17,33)(18,34)(19,36)(20,35)
(21,42)(22,41)(23,43)(24,44)(25,38)(26,37)(27,39)(28,40)(29,45)(30,46)(31,48)
(32,47)(51,52)(53,58)(54,57)(55,59)(56,60)(63,64)(65,81)(66,82)(67,84)(68,83)
(69,90)(70,89)(71,91)(72,92)(73,86)(74,85)(75,87)(76,88)(77,93)(78,94)(79,96)
(80,95);;
s1 := ( 1,65)( 2,67)( 3,66)( 4,68)( 5,69)( 6,71)( 7,70)( 8,72)( 9,79)(10,77)
(11,80)(12,78)(13,74)(14,76)(15,73)(16,75)(17,49)(18,51)(19,50)(20,52)(21,53)
(22,55)(23,54)(24,56)(25,63)(26,61)(27,64)(28,62)(29,58)(30,60)(31,57)(32,59)
(33,81)(34,83)(35,82)(36,84)(37,85)(38,87)(39,86)(40,88)(41,95)(42,93)(43,96)
(44,94)(45,90)(46,92)(47,89)(48,91);;
s2 := ( 1,13)( 2,14)( 3,16)( 4,15)( 5, 6)( 9,10)(17,45)(18,46)(19,48)(20,47)
(21,38)(22,37)(23,39)(24,40)(25,42)(26,41)(27,43)(28,44)(29,33)(30,34)(31,36)
(32,35)(49,61)(50,62)(51,64)(52,63)(53,54)(57,58)(65,93)(66,94)(67,96)(68,95)
(69,86)(70,85)(71,87)(72,88)(73,90)(74,89)(75,91)(76,92)(77,81)(78,82)(79,84)
(80,83);;
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, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(96)!( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(15,16)(17,33)(18,34)(19,36)
(20,35)(21,42)(22,41)(23,43)(24,44)(25,38)(26,37)(27,39)(28,40)(29,45)(30,46)
(31,48)(32,47)(51,52)(53,58)(54,57)(55,59)(56,60)(63,64)(65,81)(66,82)(67,84)
(68,83)(69,90)(70,89)(71,91)(72,92)(73,86)(74,85)(75,87)(76,88)(77,93)(78,94)
(79,96)(80,95);
s1 := Sym(96)!( 1,65)( 2,67)( 3,66)( 4,68)( 5,69)( 6,71)( 7,70)( 8,72)( 9,79)
(10,77)(11,80)(12,78)(13,74)(14,76)(15,73)(16,75)(17,49)(18,51)(19,50)(20,52)
(21,53)(22,55)(23,54)(24,56)(25,63)(26,61)(27,64)(28,62)(29,58)(30,60)(31,57)
(32,59)(33,81)(34,83)(35,82)(36,84)(37,85)(38,87)(39,86)(40,88)(41,95)(42,93)
(43,96)(44,94)(45,90)(46,92)(47,89)(48,91);
s2 := Sym(96)!( 1,13)( 2,14)( 3,16)( 4,15)( 5, 6)( 9,10)(17,45)(18,46)(19,48)
(20,47)(21,38)(22,37)(23,39)(24,40)(25,42)(26,41)(27,43)(28,44)(29,33)(30,34)
(31,36)(32,35)(49,61)(50,62)(51,64)(52,63)(53,54)(57,58)(65,93)(66,94)(67,96)
(68,95)(69,86)(70,85)(71,87)(72,88)(73,90)(74,89)(75,91)(76,92)(77,81)(78,82)
(79,84)(80,83);
poly := sub<Sym(96)|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, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
to this polytope