Polytope of Type {12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12}*384a
if this polytope has a name.
Group : SmallGroup(384,17873)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 16, 96, 16
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {12,12,2} of size 768
Vertex Figure Of :
   {2,12,12} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,12}*192a, {12,6}*192a
   4-fold quotients : {6,6}*96
   8-fold quotients : {3,6}*48, {6,3}*48
   12-fold quotients : {4,4}*32
   16-fold quotients : {3,3}*24
   24-fold quotients : {2,4}*16, {4,2}*16
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,12}*768a, {12,12}*768b, {12,12}*768c, {12,24}*768c, {24,12}*768c, {12,24}*768d, {24,12}*768d, {12,24}*768e, {24,12}*768e, {12,24}*768f, {24,12}*768f
   3-fold covers : {12,12}*1152j, {12,12}*1152l
   5-fold covers : {12,60}*1920c, {60,12}*1920c
Permutation Representation (GAP) :

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