Polytope of Type {3,2,24,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,24,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,98791)
Rank : 5
Schlafli Type : {3,2,24,4}
Number of vertices, edges, etc : 3, 3, 24, 48, 4
Order of s0s1s2s3s4 : 24
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 : {3,2,12,4}*576a
3-fold quotients : {3,2,8,4}*384b
4-fold quotients : {3,2,12,2}*288, {3,2,6,4}*288a
6-fold quotients : {3,2,4,4}*192
8-fold quotients : {3,2,6,2}*144
12-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96
16-fold quotients : {3,2,3,2}*72
24-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 6)( 8, 9)(10,13)(11,15)(12,14)(16,19)(17,21)(18,20)(23,24)(26,27)
(28,40)(29,42)(30,41)(31,43)(32,45)(33,44)(34,49)(35,51)(36,50)(37,46)(38,48)
(39,47)(53,54)(56,57)(58,61)(59,63)(60,62)(64,67)(65,69)(66,68)(71,72)(74,75)
(76,88)(77,90)(78,89)(79,91)(80,93)(81,92)(82,97)(83,99)(84,98)(85,94)(86,96)
(87,95);;
s3 := ( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)(10,35)(11,34)(12,36)(13,38)
(14,37)(15,39)(16,44)(17,43)(18,45)(19,41)(20,40)(21,42)(22,50)(23,49)(24,51)
(25,47)(26,46)(27,48)(52,77)(53,76)(54,78)(55,80)(56,79)(57,81)(58,83)(59,82)
(60,84)(61,86)(62,85)(63,87)(64,92)(65,91)(66,93)(67,89)(68,88)(69,90)(70,98)
(71,97)(72,99)(73,95)(74,94)(75,96);;
s4 := ( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,61)
(14,62)(15,63)(16,67)(17,68)(18,69)(19,64)(20,65)(21,66)(22,73)(23,74)(24,75)
(25,70)(26,71)(27,72)(28,82)(29,83)(30,84)(31,85)(32,86)(33,87)(34,76)(35,77)
(36,78)(37,79)(38,80)(39,81)(40,97)(41,98)(42,99)(43,94)(44,95)(45,96)(46,91)
(47,92)(48,93)(49,88)(50,89)(51,90);;
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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s4*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(99)!(2,3);
s1 := Sym(99)!(1,2);
s2 := Sym(99)!( 5, 6)( 8, 9)(10,13)(11,15)(12,14)(16,19)(17,21)(18,20)(23,24)
(26,27)(28,40)(29,42)(30,41)(31,43)(32,45)(33,44)(34,49)(35,51)(36,50)(37,46)
(38,48)(39,47)(53,54)(56,57)(58,61)(59,63)(60,62)(64,67)(65,69)(66,68)(71,72)
(74,75)(76,88)(77,90)(78,89)(79,91)(80,93)(81,92)(82,97)(83,99)(84,98)(85,94)
(86,96)(87,95);
s3 := Sym(99)!( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)(10,35)(11,34)(12,36)
(13,38)(14,37)(15,39)(16,44)(17,43)(18,45)(19,41)(20,40)(21,42)(22,50)(23,49)
(24,51)(25,47)(26,46)(27,48)(52,77)(53,76)(54,78)(55,80)(56,79)(57,81)(58,83)
(59,82)(60,84)(61,86)(62,85)(63,87)(64,92)(65,91)(66,93)(67,89)(68,88)(69,90)
(70,98)(71,97)(72,99)(73,95)(74,94)(75,96);
s4 := Sym(99)!( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)
(13,61)(14,62)(15,63)(16,67)(17,68)(18,69)(19,64)(20,65)(21,66)(22,73)(23,74)
(24,75)(25,70)(26,71)(27,72)(28,82)(29,83)(30,84)(31,85)(32,86)(33,87)(34,76)
(35,77)(36,78)(37,79)(38,80)(39,81)(40,97)(41,98)(42,99)(43,94)(44,95)(45,96)
(46,91)(47,92)(48,93)(49,88)(50,89)(51,90);
poly := sub<Sym(99)|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, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s4*s3*s4*s3*s2*s3*s2*s4*s3*s4*s3*s2*s3,
s2*s3*s2*s3*s2*s4*s3*s2*s3*s2*s4*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope