Polytope of Type {12,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6,2}*768
if this polytope has a name.
Group : SmallGroup(768,1089251)
Rank : 4
Schlafli Type : {12,6,2}
Number of vertices, edges, etc : 32, 96, 16, 2
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,6,2}*384a, {12,6,2}*384b, {6,6,2}*384b
   4-fold quotients : {12,3,2}*192, {6,6,2}*192
   8-fold quotients : {3,6,2}*96, {6,3,2}*96
   16-fold quotients : {3,3,2}*48
   24-fold quotients : {4,2,2}*32
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1,49)( 2,50)( 3,54)( 4,53)( 5,52)( 6,51)( 7,56)( 8,55)( 9,65)(10,66)
(11,70)(12,69)(13,68)(14,67)(15,72)(16,71)(17,57)(18,58)(19,62)(20,61)(21,60)
(22,59)(23,64)(24,63)(25,73)(26,74)(27,78)(28,77)(29,76)(30,75)(31,80)(32,79)
(33,89)(34,90)(35,94)(36,93)(37,92)(38,91)(39,96)(40,95)(41,81)(42,82)(43,86)
(44,85)(45,84)(46,83)(47,88)(48,87);;
s1 := ( 1, 9)( 2,10)( 3,12)( 4,11)( 5,15)( 6,16)( 7,13)( 8,14)(19,20)(21,23)
(22,24)(25,33)(26,34)(27,36)(28,35)(29,39)(30,40)(31,37)(32,38)(43,44)(45,47)
(46,48)(49,82)(50,81)(51,83)(52,84)(53,88)(54,87)(55,86)(56,85)(57,74)(58,73)
(59,75)(60,76)(61,80)(62,79)(63,78)(64,77)(65,90)(66,89)(67,91)(68,92)(69,96)
(70,95)(71,94)(72,93);;
s2 := ( 1, 7)( 2, 8)( 5, 6)( 9,23)(10,24)(11,19)(12,20)(13,22)(14,21)(15,17)
(16,18)(25,31)(26,32)(29,30)(33,47)(34,48)(35,43)(36,44)(37,46)(38,45)(39,41)
(40,42)(49,56)(50,55)(51,52)(57,72)(58,71)(59,68)(60,67)(61,69)(62,70)(63,66)
(64,65)(73,80)(74,79)(75,76)(81,96)(82,95)(83,92)(84,91)(85,93)(86,94)(87,90)
(88,89);;
s3 := (97,98);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(98)!( 1,49)( 2,50)( 3,54)( 4,53)( 5,52)( 6,51)( 7,56)( 8,55)( 9,65)
(10,66)(11,70)(12,69)(13,68)(14,67)(15,72)(16,71)(17,57)(18,58)(19,62)(20,61)
(21,60)(22,59)(23,64)(24,63)(25,73)(26,74)(27,78)(28,77)(29,76)(30,75)(31,80)
(32,79)(33,89)(34,90)(35,94)(36,93)(37,92)(38,91)(39,96)(40,95)(41,81)(42,82)
(43,86)(44,85)(45,84)(46,83)(47,88)(48,87);
s1 := Sym(98)!( 1, 9)( 2,10)( 3,12)( 4,11)( 5,15)( 6,16)( 7,13)( 8,14)(19,20)
(21,23)(22,24)(25,33)(26,34)(27,36)(28,35)(29,39)(30,40)(31,37)(32,38)(43,44)
(45,47)(46,48)(49,82)(50,81)(51,83)(52,84)(53,88)(54,87)(55,86)(56,85)(57,74)
(58,73)(59,75)(60,76)(61,80)(62,79)(63,78)(64,77)(65,90)(66,89)(67,91)(68,92)
(69,96)(70,95)(71,94)(72,93);
s2 := Sym(98)!( 1, 7)( 2, 8)( 5, 6)( 9,23)(10,24)(11,19)(12,20)(13,22)(14,21)
(15,17)(16,18)(25,31)(26,32)(29,30)(33,47)(34,48)(35,43)(36,44)(37,46)(38,45)
(39,41)(40,42)(49,56)(50,55)(51,52)(57,72)(58,71)(59,68)(60,67)(61,69)(62,70)
(63,66)(64,65)(73,80)(74,79)(75,76)(81,96)(82,95)(83,92)(84,91)(85,93)(86,94)
(87,90)(88,89);
s3 := Sym(98)!(97,98);
poly := sub<Sym(98)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope