Polytope of Type {2,24,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,4}*384a
if this polytope has a name.
Group : SmallGroup(384,11182)
Rank : 4
Schlafli Type : {2,24,4}
Number of vertices, edges, etc : 2, 24, 48, 4
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,24,4,2} of size 768
Vertex Figure Of :
   {2,2,24,4} of size 768
   {3,2,24,4} of size 1152
   {5,2,24,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,12,4}*192a, {2,24,2}*192
   3-fold quotients : {2,8,4}*128a
   4-fold quotients : {2,12,2}*96, {2,6,4}*96a
   6-fold quotients : {2,4,4}*64, {2,8,2}*64
   8-fold quotients : {2,6,2}*48
   12-fold quotients : {2,2,4}*32, {2,4,2}*32
   16-fold quotients : {2,3,2}*24
   24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,24,4}*768a, {2,24,8}*768b, {2,24,8}*768c, {4,24,4}*768d, {2,48,4}*768a, {2,48,4}*768b
   3-fold covers : {2,72,4}*1152a, {6,24,4}*1152b, {6,24,4}*1152c, {2,24,12}*1152a, {2,24,12}*1152b
   5-fold covers : {2,120,4}*1920a, {10,24,4}*1920a, {2,24,20}*1920a
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(15,18)(16,20)(17,19)(21,24)(22,26)(23,25)
(27,39)(28,41)(29,40)(30,42)(31,44)(32,43)(33,45)(34,47)(35,46)(36,48)(37,50)
(38,49)(52,53)(55,56)(58,59)(61,62)(63,66)(64,68)(65,67)(69,72)(70,74)(71,73)
(75,87)(76,89)(77,88)(78,90)(79,92)(80,91)(81,93)(82,95)(83,94)(84,96)(85,98)
(86,97);;
s2 := ( 3,28)( 4,27)( 5,29)( 6,31)( 7,30)( 8,32)( 9,34)(10,33)(11,35)(12,37)
(13,36)(14,38)(15,43)(16,42)(17,44)(18,40)(19,39)(20,41)(21,49)(22,48)(23,50)
(24,46)(25,45)(26,47)(51,76)(52,75)(53,77)(54,79)(55,78)(56,80)(57,82)(58,81)
(59,83)(60,85)(61,84)(62,86)(63,91)(64,90)(65,92)(66,88)(67,87)(68,89)(69,97)
(70,96)(71,98)(72,94)(73,93)(74,95);;
s3 := ( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)
(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,70)(23,71)
(24,72)(25,73)(26,74)(27,81)(28,82)(29,83)(30,84)(31,85)(32,86)(33,75)(34,76)
(35,77)(36,78)(37,79)(38,80)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,87)
(46,88)(47,89)(48,90)(49,91)(50,92);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 4, 5)( 7, 8)(10,11)(13,14)(15,18)(16,20)(17,19)(21,24)(22,26)
(23,25)(27,39)(28,41)(29,40)(30,42)(31,44)(32,43)(33,45)(34,47)(35,46)(36,48)
(37,50)(38,49)(52,53)(55,56)(58,59)(61,62)(63,66)(64,68)(65,67)(69,72)(70,74)
(71,73)(75,87)(76,89)(77,88)(78,90)(79,92)(80,91)(81,93)(82,95)(83,94)(84,96)
(85,98)(86,97);
s2 := Sym(98)!( 3,28)( 4,27)( 5,29)( 6,31)( 7,30)( 8,32)( 9,34)(10,33)(11,35)
(12,37)(13,36)(14,38)(15,43)(16,42)(17,44)(18,40)(19,39)(20,41)(21,49)(22,48)
(23,50)(24,46)(25,45)(26,47)(51,76)(52,75)(53,77)(54,79)(55,78)(56,80)(57,82)
(58,81)(59,83)(60,85)(61,84)(62,86)(63,91)(64,90)(65,92)(66,88)(67,87)(68,89)
(69,97)(70,96)(71,98)(72,94)(73,93)(74,95);
s3 := Sym(98)!( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)
(12,60)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)(22,70)
(23,71)(24,72)(25,73)(26,74)(27,81)(28,82)(29,83)(30,84)(31,85)(32,86)(33,75)
(34,76)(35,77)(36,78)(37,79)(38,80)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)
(45,87)(46,88)(47,89)(48,90)(49,91)(50,92);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope