Polytope of Type {12,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8,2}*768g
if this polytope has a name.
Group : SmallGroup(768,1089251)
Rank : 4
Schlafli Type : {12,8,2}
Number of vertices, edges, etc : 24, 96, 16, 2
Order of s₀s₁s₂s₃ : 6
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 : {12,4,2}*384c, {6,8,2}*384c
   4-fold quotients : {6,4,2}*192
   8-fold quotients : {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   16-fold quotients : {3,4,2}*48, {6,2,2}*48
   32-fold quotients : {3,2,2}*24
   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 := ( 1,55)( 2,56)( 3,53)( 4,54)( 5,52)( 6,51)( 7,50)( 8,49)( 9,63)(10,64)
(11,61)(12,62)(13,60)(14,59)(15,58)(16,57)(17,71)(18,72)(19,69)(20,70)(21,68)
(22,67)(23,66)(24,65)(25,79)(26,80)(27,77)(28,78)(29,76)(30,75)(31,74)(32,73)
(33,87)(34,88)(35,85)(36,86)(37,84)(38,83)(39,82)(40,81)(41,95)(42,96)(43,93)
(44,94)(45,92)(46,91)(47,90)(48,89);;
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, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*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(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)!( 1,55)( 2,56)( 3,53)( 4,54)( 5,52)( 6,51)( 7,50)( 8,49)( 9,63)
(10,64)(11,61)(12,62)(13,60)(14,59)(15,58)(16,57)(17,71)(18,72)(19,69)(20,70)
(21,68)(22,67)(23,66)(24,65)(25,79)(26,80)(27,77)(28,78)(29,76)(30,75)(31,74)
(32,73)(33,87)(34,88)(35,85)(36,86)(37,84)(38,83)(39,82)(40,81)(41,95)(42,96)
(43,93)(44,94)(45,92)(46,91)(47,90)(48,89);
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, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

to this polytope