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