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# Polytope of Type {6,4,4}

Atlas Canonical Name : {6,4,4}*384b
if this polytope has a name.
Group : SmallGroup(384,17948)
Rank : 4
Schlafli Type : {6,4,4}
Number of vertices, edges, etc : 6, 24, 16, 8
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 4
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,4,4,2} of size 768
{6,4,4,3} of size 1152
Vertex Figure Of :
{2,6,4,4} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,4,4}*192a
4-fold quotients : {6,4,2}*96c
8-fold quotients : {3,4,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,4,4}*768c, {12,4,4}*768d, {6,4,4}*768c, {6,4,4}*768f
3-fold covers : {18,4,4}*1152b
5-fold covers : {30,4,4}*1920b
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(15,16)(17,33)(18,34)(19,36)(20,35)
(21,41)(22,42)(23,44)(24,43)(25,37)(26,38)(27,40)(28,39)(29,45)(30,46)(31,48)
(32,47)(51,52)(53,57)(54,58)(55,60)(56,59)(63,64)(65,81)(66,82)(67,84)(68,83)
(69,89)(70,90)(71,92)(72,91)(73,85)(74,86)(75,88)(76,87)(77,93)(78,94)(79,96)
(80,95);;
s1 := ( 1,65)( 2,68)( 3,67)( 4,66)( 5,69)( 6,72)( 7,71)( 8,70)( 9,77)(10,80)
(11,79)(12,78)(13,73)(14,76)(15,75)(16,74)(17,49)(18,52)(19,51)(20,50)(21,53)
(22,56)(23,55)(24,54)(25,61)(26,64)(27,63)(28,62)(29,57)(30,60)(31,59)(32,58)
(33,81)(34,84)(35,83)(36,82)(37,85)(38,88)(39,87)(40,86)(41,93)(42,96)(43,95)
(44,94)(45,89)(46,92)(47,91)(48,90);;
s2 := ( 1,13)( 2,14)( 3,15)( 4,16)( 5, 9)( 6,10)( 7,11)( 8,12)(17,29)(18,30)
(19,31)(20,32)(21,25)(22,26)(23,27)(24,28)(33,45)(34,46)(35,47)(36,48)(37,41)
(38,42)(39,43)(40,44)(49,61)(50,62)(51,63)(52,64)(53,57)(54,58)(55,59)(56,60)
(65,77)(66,78)(67,79)(68,80)(69,73)(70,74)(71,75)(72,76)(81,93)(82,94)(83,95)
(84,96)(85,89)(86,90)(87,91)(88,92);;
s3 := ( 5, 7)( 6, 8)( 9,12)(10,11)(13,14)(15,16)(21,23)(22,24)(25,28)(26,27)
(29,30)(31,32)(37,39)(38,40)(41,44)(42,43)(45,46)(47,48)(53,55)(54,56)(57,60)
(58,59)(61,62)(63,64)(69,71)(70,72)(73,76)(74,75)(77,78)(79,80)(85,87)(86,88)
(89,92)(90,91)(93,94)(95,96);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s1*s0*s2*s1*s2*s1*s0*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

References : None.
to this polytope