Polytope of Type {2,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,12}*768a
if this polytope has a name.
Group : SmallGroup(768,323570)
Rank : 4
Schlafli Type : {2,4,12}
Number of vertices, edges, etc : 2, 16, 96, 48
Order of s₀s₁s₂s₃ : 24
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 : {2,4,12}*384a
   3-fold quotients : {2,4,4}*256
   4-fold quotients : {2,4,12}*192a
   6-fold quotients : {2,4,4}*128
   8-fold quotients : {2,2,12}*96, {2,4,6}*96a
   12-fold quotients : {2,4,4}*64
   16-fold quotients : {2,2,6}*48
   24-fold quotients : {2,2,4}*32, {2,4,2}*32
   32-fold quotients : {2,2,3}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope