Polytope of Type {2,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,4}*768d
if this polytope has a name.
Group : SmallGroup(768,1088705)
Rank : 4
Schlafli Type : {2,12,4}
Number of vertices, edges, etc : 2, 48, 96, 16
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 : {2,12,4}*384b, {2,6,4}*384b, {2,12,4}*384c
4-fold quotients : {2,12,4}*192a, {2,12,4}*192b, {2,12,4}*192c, {2,6,4}*192
8-fold quotients : {2,12,2}*96, {2,6,4}*96a, {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
12-fold quotients : {2,4,4}*64
16-fold quotients : {2,3,4}*48, {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 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)(22,26)
(28,29)(31,35)(32,37)(33,36)(34,38)(40,41)(43,47)(44,49)(45,48)(46,50)(51,75)
(52,77)(53,76)(54,78)(55,83)(56,85)(57,84)(58,86)(59,79)(60,81)(61,80)(62,82)
(63,87)(64,89)(65,88)(66,90)(67,95)(68,97)(69,96)(70,98)(71,91)(72,93)(73,92)
(74,94);;
s2 := ( 3,55)( 4,56)( 5,58)( 6,57)( 7,51)( 8,52)( 9,54)(10,53)(11,59)(12,60)
(13,62)(14,61)(15,67)(16,68)(17,70)(18,69)(19,63)(20,64)(21,66)(22,65)(23,71)
(24,72)(25,74)(26,73)(27,79)(28,80)(29,82)(30,81)(31,75)(32,76)(33,78)(34,77)
(35,83)(36,84)(37,86)(38,85)(39,91)(40,92)(41,94)(42,93)(43,87)(44,88)(45,90)
(46,89)(47,95)(48,96)(49,98)(50,97);;
s3 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)(20,21)
(23,26)(24,25)(27,30)(28,29)(31,34)(32,33)(35,38)(36,37)(39,42)(40,41)(43,46)
(44,45)(47,50)(48,49)(51,66)(52,65)(53,64)(54,63)(55,70)(56,69)(57,68)(58,67)
(59,74)(60,73)(61,72)(62,71)(75,90)(76,89)(77,88)(78,87)(79,94)(80,93)(81,92)
(82,91)(83,98)(84,97)(85,96)(86,95);;
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*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s3*s2*s3*s2*s1*s2*s1*s2*s1*s3*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*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)
(22,26)(28,29)(31,35)(32,37)(33,36)(34,38)(40,41)(43,47)(44,49)(45,48)(46,50)
(51,75)(52,77)(53,76)(54,78)(55,83)(56,85)(57,84)(58,86)(59,79)(60,81)(61,80)
(62,82)(63,87)(64,89)(65,88)(66,90)(67,95)(68,97)(69,96)(70,98)(71,91)(72,93)
(73,92)(74,94);
s2 := Sym(98)!( 3,55)( 4,56)( 5,58)( 6,57)( 7,51)( 8,52)( 9,54)(10,53)(11,59)
(12,60)(13,62)(14,61)(15,67)(16,68)(17,70)(18,69)(19,63)(20,64)(21,66)(22,65)
(23,71)(24,72)(25,74)(26,73)(27,79)(28,80)(29,82)(30,81)(31,75)(32,76)(33,78)
(34,77)(35,83)(36,84)(37,86)(38,85)(39,91)(40,92)(41,94)(42,93)(43,87)(44,88)
(45,90)(46,89)(47,95)(48,96)(49,98)(50,97);
s3 := Sym(98)!( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)
(20,21)(23,26)(24,25)(27,30)(28,29)(31,34)(32,33)(35,38)(36,37)(39,42)(40,41)
(43,46)(44,45)(47,50)(48,49)(51,66)(52,65)(53,64)(54,63)(55,70)(56,69)(57,68)
(58,67)(59,74)(60,73)(61,72)(62,71)(75,90)(76,89)(77,88)(78,87)(79,94)(80,93)
(81,92)(82,91)(83,98)(84,97)(85,96)(86,95);
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*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s3*s2*s3*s2*s1*s2*s1*s2*s1*s3*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*s1*s2*s1*s2 >;
to this polytope