Polytope of Type {12,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8,2}*768b
if this polytope has a name.
Group : SmallGroup(768,323571)
Rank : 4
Schlafli Type : {12,8,2}
Number of vertices, edges, etc : 24, 96, 16, 2
Order of s₀s₁s₂s₃ : 12
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}*384a
   3-fold quotients : {4,8,2}*256b
   4-fold quotients : {12,4,2}*192a
   6-fold quotients : {4,4,2}*128
   8-fold quotients : {12,2,2}*96, {6,4,2}*96a
   12-fold quotients : {4,4,2}*64
   16-fold quotients : {6,2,2}*48
   24-fold quotients : {2,4,2}*32, {4,2,2}*32
   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)( 2,51)( 3,50)( 4,52)( 5,54)( 6,53)( 7,55)( 8,57)( 9,56)(10,58)
(11,60)(12,59)(13,70)(14,72)(15,71)(16,67)(17,69)(18,68)(19,64)(20,66)(21,65)
(22,61)(23,63)(24,62)(25,73)(26,75)(27,74)(28,76)(29,78)(30,77)(31,79)(32,81)
(33,80)(34,82)(35,84)(36,83)(37,94)(38,96)(39,95)(40,91)(41,93)(42,92)(43,88)
(44,90)(45,89)(46,85)(47,87)(48,86);;
s1 := ( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,14)(16,17)(19,23)(20,22)(21,24)
(25,38)(26,37)(27,39)(28,41)(29,40)(30,42)(31,47)(32,46)(33,48)(34,44)(35,43)
(36,45)(49,50)(52,53)(55,59)(56,58)(57,60)(61,62)(64,65)(67,71)(68,70)(69,72)
(73,86)(74,85)(75,87)(76,89)(77,88)(78,90)(79,95)(80,94)(81,96)(82,92)(83,91)
(84,93);;
s2 := ( 1,73)( 2,74)( 3,75)( 4,76)( 5,77)( 6,78)( 7,79)( 8,80)( 9,81)(10,82)
(11,83)(12,84)(13,94)(14,95)(15,96)(16,91)(17,92)(18,93)(19,88)(20,89)(21,90)
(22,85)(23,86)(24,87)(25,49)(26,50)(27,51)(28,52)(29,53)(30,54)(31,55)(32,56)
(33,57)(34,58)(35,59)(36,60)(37,70)(38,71)(39,72)(40,67)(41,68)(42,69)(43,64)
(44,65)(45,66)(46,61)(47,62)(48,63);;
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*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope