Polytope of Type {3,12,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,12,4,2}*768
if this polytope has a name.
Group : SmallGroup(768,1089251)
Rank : 5
Schlafli Type : {3,12,4,2}
Number of vertices, edges, etc : 4, 24, 32, 4, 2
Order of s0s1s2s3s4 : 8
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 : {3,6,4,2}*384, {3,12,2,2}*384
4-fold quotients : {3,6,2,2}*192
8-fold quotients : {3,3,2,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 6)( 4, 5)( 7, 8)( 9,17)(10,18)(11,22)(12,21)(13,20)(14,19)(15,24)
(16,23)(27,30)(28,29)(31,32)(33,41)(34,42)(35,46)(36,45)(37,44)(38,43)(39,48)
(40,47)(49,50)(51,53)(52,54)(57,66)(58,65)(59,69)(60,70)(61,67)(62,68)(63,71)
(64,72)(73,74)(75,77)(76,78)(81,90)(82,89)(83,93)(84,94)(85,91)(86,92)(87,95)
(88,96);;
s1 := ( 1, 9)( 2,10)( 3,12)( 4,11)( 5,15)( 6,16)( 7,13)( 8,14)(19,20)(21,23)
(22,24)(25,33)(26,34)(27,36)(28,35)(29,39)(30,40)(31,37)(32,38)(43,44)(45,47)
(46,48)(49,58)(50,57)(51,59)(52,60)(53,64)(54,63)(55,62)(56,61)(65,66)(69,72)
(70,71)(73,82)(74,81)(75,83)(76,84)(77,88)(78,87)(79,86)(80,85)(89,90)(93,96)
(94,95);;
s2 := ( 1,55)( 2,56)( 3,51)( 4,52)( 5,54)( 6,53)( 7,49)( 8,50)( 9,71)(10,72)
(11,67)(12,68)(13,70)(14,69)(15,65)(16,66)(17,63)(18,64)(19,59)(20,60)(21,62)
(22,61)(23,57)(24,58)(25,79)(26,80)(27,75)(28,76)(29,78)(30,77)(31,73)(32,74)
(33,95)(34,96)(35,91)(36,92)(37,94)(38,93)(39,89)(40,90)(41,87)(42,88)(43,83)
(44,84)(45,86)(46,85)(47,81)(48,82);;
s3 := (49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,79)(56,80)(57,81)(58,82)
(59,83)(60,84)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)
(70,94)(71,95)(72,96);;
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,
s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(98)!( 3, 6)( 4, 5)( 7, 8)( 9,17)(10,18)(11,22)(12,21)(13,20)(14,19)
(15,24)(16,23)(27,30)(28,29)(31,32)(33,41)(34,42)(35,46)(36,45)(37,44)(38,43)
(39,48)(40,47)(49,50)(51,53)(52,54)(57,66)(58,65)(59,69)(60,70)(61,67)(62,68)
(63,71)(64,72)(73,74)(75,77)(76,78)(81,90)(82,89)(83,93)(84,94)(85,91)(86,92)
(87,95)(88,96);
s1 := Sym(98)!( 1, 9)( 2,10)( 3,12)( 4,11)( 5,15)( 6,16)( 7,13)( 8,14)(19,20)
(21,23)(22,24)(25,33)(26,34)(27,36)(28,35)(29,39)(30,40)(31,37)(32,38)(43,44)
(45,47)(46,48)(49,58)(50,57)(51,59)(52,60)(53,64)(54,63)(55,62)(56,61)(65,66)
(69,72)(70,71)(73,82)(74,81)(75,83)(76,84)(77,88)(78,87)(79,86)(80,85)(89,90)
(93,96)(94,95);
s2 := Sym(98)!( 1,55)( 2,56)( 3,51)( 4,52)( 5,54)( 6,53)( 7,49)( 8,50)( 9,71)
(10,72)(11,67)(12,68)(13,70)(14,69)(15,65)(16,66)(17,63)(18,64)(19,59)(20,60)
(21,62)(22,61)(23,57)(24,58)(25,79)(26,80)(27,75)(28,76)(29,78)(30,77)(31,73)
(32,74)(33,95)(34,96)(35,91)(36,92)(37,94)(38,93)(39,89)(40,90)(41,87)(42,88)
(43,83)(44,84)(45,86)(46,85)(47,81)(48,82);
s3 := Sym(98)!(49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,79)(56,80)(57,81)
(58,82)(59,83)(60,84)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)
(69,93)(70,94)(71,95)(72,96);
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, s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 >;
to this polytope