Polytope of Type {2,12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6}*768
if this polytope has a name.
Group : SmallGroup(768,1089251)
Rank : 4
Schlafli Type : {2,12,6}
Number of vertices, edges, etc : 2, 32, 96, 16
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 : {2,12,6}*384a, {2,12,6}*384b, {2,6,6}*384b
   4-fold quotients : {2,12,3}*192, {2,6,6}*192
   8-fold quotients : {2,3,6}*96, {2,6,3}*96
   16-fold quotients : {2,3,3}*48
   24-fold quotients : {2,4,2}*32
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope