Polytope of Type {2,12,4}

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

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

Permutation Representation (Magma) :

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

to this polytope