Polytope of Type {24,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4,2}*384b
if this polytope has a name.
Group : SmallGroup(384,11274)
Rank : 4
Schlafli Type : {24,4,2}
Number of vertices, edges, etc : 24, 48, 4, 2
Order of s0s1s2s3 : 24
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{24,4,2,2} of size 768
{24,4,2,3} of size 1152
{24,4,2,5} of size 1920
Vertex Figure Of :
{2,24,4,2} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,4,2}*192a
3-fold quotients : {8,4,2}*128b
4-fold quotients : {12,2,2}*96, {6,4,2}*96a
6-fold quotients : {4,4,2}*64
8-fold quotients : {6,2,2}*48
12-fold quotients : {2,4,2}*32, {4,2,2}*32
16-fold quotients : {3,2,2}*24
24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {24,4,2}*768a, {24,8,2}*768a, {24,8,2}*768d, {24,4,4}*768b
3-fold covers : {72,4,2}*1152b, {24,4,6}*1152b, {24,12,2}*1152d, {24,12,2}*1152e
5-fold covers : {120,4,2}*1920b, {24,4,10}*1920b, {24,20,2}*1920b
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 6)( 7,10)( 8,12)( 9,11)(13,16)(14,18)(15,17)(20,21)(23,24)
(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,46)(32,48)(33,47)(34,43)(35,45)
(36,44)(50,51)(53,54)(55,58)(56,60)(57,59)(61,64)(62,66)(63,65)(68,69)(71,72)
(73,85)(74,87)(75,86)(76,88)(77,90)(78,89)(79,94)(80,96)(81,95)(82,91)(83,93)
(84,92);;
s1 := ( 1,26)( 2,25)( 3,27)( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)(10,35)
(11,34)(12,36)(13,41)(14,40)(15,42)(16,38)(17,37)(18,39)(19,47)(20,46)(21,48)
(22,44)(23,43)(24,45)(49,74)(50,73)(51,75)(52,77)(53,76)(54,78)(55,80)(56,79)
(57,81)(58,83)(59,82)(60,84)(61,89)(62,88)(63,90)(64,86)(65,85)(66,87)(67,95)
(68,94)(69,96)(70,92)(71,91)(72,93);;
s2 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)
(11,59)(12,60)(13,64)(14,65)(15,66)(16,61)(17,62)(18,63)(19,70)(20,71)(21,72)
(22,67)(23,68)(24,69)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,73)(32,74)
(33,75)(34,76)(35,77)(36,78)(37,94)(38,95)(39,96)(40,91)(41,92)(42,93)(43,88)
(44,89)(45,90)(46,85)(47,86)(48,87);;
s3 := (97,98);;
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, s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(98)!( 2, 3)( 5, 6)( 7,10)( 8,12)( 9,11)(13,16)(14,18)(15,17)(20,21)
(23,24)(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,46)(32,48)(33,47)(34,43)
(35,45)(36,44)(50,51)(53,54)(55,58)(56,60)(57,59)(61,64)(62,66)(63,65)(68,69)
(71,72)(73,85)(74,87)(75,86)(76,88)(77,90)(78,89)(79,94)(80,96)(81,95)(82,91)
(83,93)(84,92);
s1 := Sym(98)!( 1,26)( 2,25)( 3,27)( 4,29)( 5,28)( 6,30)( 7,32)( 8,31)( 9,33)
(10,35)(11,34)(12,36)(13,41)(14,40)(15,42)(16,38)(17,37)(18,39)(19,47)(20,46)
(21,48)(22,44)(23,43)(24,45)(49,74)(50,73)(51,75)(52,77)(53,76)(54,78)(55,80)
(56,79)(57,81)(58,83)(59,82)(60,84)(61,89)(62,88)(63,90)(64,86)(65,85)(66,87)
(67,95)(68,94)(69,96)(70,92)(71,91)(72,93);
s2 := Sym(98)!( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)
(10,58)(11,59)(12,60)(13,64)(14,65)(15,66)(16,61)(17,62)(18,63)(19,70)(20,71)
(21,72)(22,67)(23,68)(24,69)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,73)
(32,74)(33,75)(34,76)(35,77)(36,78)(37,94)(38,95)(39,96)(40,91)(41,92)(42,93)
(43,88)(44,89)(45,90)(46,85)(47,86)(48,87);
s3 := Sym(98)!(97,98);
poly := sub<Sym(98)|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,
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope