Polytope of Type {2,8,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,12}*768b
if this polytope has a name.
Group : SmallGroup(768,323571)
Rank : 4
Schlafli Type : {2,8,12}
Number of vertices, edges, etc : 2, 16, 96, 24
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 : {2,4,12}*384a
3-fold quotients : {2,8,4}*256b
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 := ( 3,75)( 4,76)( 5,77)( 6,78)( 7,79)( 8,80)( 9,81)(10,82)(11,83)(12,84)
(13,85)(14,86)(15,96)(16,97)(17,98)(18,93)(19,94)(20,95)(21,90)(22,91)(23,92)
(24,87)(25,88)(26,89)(27,51)(28,52)(29,53)(30,54)(31,55)(32,56)(33,57)(34,58)
(35,59)(36,60)(37,61)(38,62)(39,72)(40,73)(41,74)(42,69)(43,70)(44,71)(45,66)
(46,67)(47,68)(48,63)(49,64)(50,65);;
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,
s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*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)!( 3,75)( 4,76)( 5,77)( 6,78)( 7,79)( 8,80)( 9,81)(10,82)(11,83)
(12,84)(13,85)(14,86)(15,96)(16,97)(17,98)(18,93)(19,94)(20,95)(21,90)(22,91)
(23,92)(24,87)(25,88)(26,89)(27,51)(28,52)(29,53)(30,54)(31,55)(32,56)(33,57)
(34,58)(35,59)(36,60)(37,61)(38,62)(39,72)(40,73)(41,74)(42,69)(43,70)(44,71)
(45,66)(46,67)(47,68)(48,63)(49,64)(50,65);
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, s3*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*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