Polytope of Type {4,4,3,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,3,2}*768b
if this polytope has a name.
Group : SmallGroup(768,1089108)
Rank : 5
Schlafli Type : {4,4,3,2}
Number of vertices, edges, etc : 8, 32, 24, 6, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 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 : {4,4,3,2}*384a
4-fold quotients : {2,4,3,2}*192
8-fold quotients : {2,4,3,2}*96
16-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 1,57)( 2,58)( 3,59)( 4,60)( 5,61)( 6,62)( 7,63)( 8,64)( 9,49)(10,50)
(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,73)(18,74)(19,75)(20,76)(21,77)
(22,78)(23,79)(24,80)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)
(33,89)(34,90)(35,91)(36,92)(37,93)(38,94)(39,95)(40,96)(41,81)(42,82)(43,83)
(44,84)(45,85)(46,86)(47,87)(48,88);;
s2 := ( 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);;
s3 := ( 1,33)( 2,35)( 3,34)( 4,36)( 5,45)( 6,47)( 7,46)( 8,48)( 9,41)(10,43)
(11,42)(12,44)(13,37)(14,39)(15,38)(16,40)(18,19)(21,29)(22,31)(23,30)(24,32)
(26,27)(49,81)(50,83)(51,82)(52,84)(53,93)(54,95)(55,94)(56,96)(57,89)(58,91)
(59,90)(60,92)(61,85)(62,87)(63,86)(64,88)(66,67)(69,77)(70,79)(71,78)(72,80)
(74,75);;
s4 := (97,98);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s2*s3*s1*s2*s1*s0*s1*s2*s3*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(98)!( 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);
s1 := Sym(98)!( 1,57)( 2,58)( 3,59)( 4,60)( 5,61)( 6,62)( 7,63)( 8,64)( 9,49)
(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,73)(18,74)(19,75)(20,76)
(21,77)(22,78)(23,79)(24,80)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)
(32,72)(33,89)(34,90)(35,91)(36,92)(37,93)(38,94)(39,95)(40,96)(41,81)(42,82)
(43,83)(44,84)(45,85)(46,86)(47,87)(48,88);
s2 := Sym(98)!( 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);
s3 := Sym(98)!( 1,33)( 2,35)( 3,34)( 4,36)( 5,45)( 6,47)( 7,46)( 8,48)( 9,41)
(10,43)(11,42)(12,44)(13,37)(14,39)(15,38)(16,40)(18,19)(21,29)(22,31)(23,30)
(24,32)(26,27)(49,81)(50,83)(51,82)(52,84)(53,93)(54,95)(55,94)(56,96)(57,89)
(58,91)(59,90)(60,92)(61,85)(62,87)(63,86)(64,88)(66,67)(69,77)(70,79)(71,78)
(72,80)(74,75);
s4 := Sym(98)!(97,98);
poly := sub<Sym(98)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s2*s3*s1*s2*s1*s0*s1*s2*s3*s1*s2*s1 >;
to this polytope