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# Polytope of Type {2,12,4}

Atlas Canonical Name : {2,12,4}*384b
if this polytope has a name.
Group : SmallGroup(384,20049)
Rank : 4
Schlafli Type : {2,12,4}
Number of vertices, edges, etc : 2, 24, 48, 8
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,12,4,2} of size 768
Vertex Figure Of :
{2,2,12,4} of size 768
{3,2,12,4} of size 1152
{5,2,12,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,12,4}*192b, {2,12,4}*192c, {2,6,4}*192
4-fold quotients : {2,12,2}*96, {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
8-fold quotients : {2,3,4}*48, {2,6,2}*48
12-fold quotients : {2,4,2}*32
16-fold quotients : {2,3,2}*24
24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,12,4}*768e, {2,12,4}*768d, {2,12,8}*768e, {2,12,8}*768f, {2,24,4}*768c, {2,24,4}*768d
3-fold covers : {2,36,4}*1152b, {6,12,4}*1152e, {6,12,4}*1152f, {2,12,12}*1152d, {2,12,12}*1152e
5-fold covers : {10,12,4}*1920b, {2,12,20}*1920b, {2,60,4}*1920b
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)
(27,39)(28,41)(29,40)(30,42)(31,47)(32,49)(33,48)(34,50)(35,43)(36,45)(37,44)
(38,46)(52,53)(55,59)(56,61)(57,60)(58,62)(64,65)(67,71)(68,73)(69,72)(70,74)
(75,87)(76,89)(77,88)(78,90)(79,95)(80,97)(81,96)(82,98)(83,91)(84,93)(85,92)
(86,94);;
s2 := ( 3,31)( 4,32)( 5,34)( 6,33)( 7,27)( 8,28)( 9,30)(10,29)(11,35)(12,36)
(13,38)(14,37)(15,43)(16,44)(17,46)(18,45)(19,39)(20,40)(21,42)(22,41)(23,47)
(24,48)(25,50)(26,49)(51,79)(52,80)(53,82)(54,81)(55,75)(56,76)(57,78)(58,77)
(59,83)(60,84)(61,86)(62,85)(63,91)(64,92)(65,94)(66,93)(67,87)(68,88)(69,90)
(70,89)(71,95)(72,96)(73,98)(74,97);;
s3 := ( 3,54)( 4,53)( 5,52)( 6,51)( 7,58)( 8,57)( 9,56)(10,55)(11,62)(12,61)
(13,60)(14,59)(15,66)(16,65)(17,64)(18,63)(19,70)(20,69)(21,68)(22,67)(23,74)
(24,73)(25,72)(26,71)(27,78)(28,77)(29,76)(30,75)(31,82)(32,81)(33,80)(34,79)
(35,86)(36,85)(37,84)(38,83)(39,90)(40,89)(41,88)(42,87)(43,94)(44,93)(45,92)
(46,91)(47,98)(48,97)(49,96)(50,95);;
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*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*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)(27,39)(28,41)(29,40)(30,42)(31,47)(32,49)(33,48)(34,50)(35,43)(36,45)
(37,44)(38,46)(52,53)(55,59)(56,61)(57,60)(58,62)(64,65)(67,71)(68,73)(69,72)
(70,74)(75,87)(76,89)(77,88)(78,90)(79,95)(80,97)(81,96)(82,98)(83,91)(84,93)
(85,92)(86,94);
s2 := Sym(98)!( 3,31)( 4,32)( 5,34)( 6,33)( 7,27)( 8,28)( 9,30)(10,29)(11,35)
(12,36)(13,38)(14,37)(15,43)(16,44)(17,46)(18,45)(19,39)(20,40)(21,42)(22,41)
(23,47)(24,48)(25,50)(26,49)(51,79)(52,80)(53,82)(54,81)(55,75)(56,76)(57,78)
(58,77)(59,83)(60,84)(61,86)(62,85)(63,91)(64,92)(65,94)(66,93)(67,87)(68,88)
(69,90)(70,89)(71,95)(72,96)(73,98)(74,97);
s3 := Sym(98)!( 3,54)( 4,53)( 5,52)( 6,51)( 7,58)( 8,57)( 9,56)(10,55)(11,62)
(12,61)(13,60)(14,59)(15,66)(16,65)(17,64)(18,63)(19,70)(20,69)(21,68)(22,67)
(23,74)(24,73)(25,72)(26,71)(27,78)(28,77)(29,76)(30,75)(31,82)(32,81)(33,80)
(34,79)(35,86)(36,85)(37,84)(38,83)(39,90)(40,89)(41,88)(42,87)(43,94)(44,93)
(45,92)(46,91)(47,98)(48,97)(49,96)(50,95);
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*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*s1*s2 >;

to this polytope