Polytope of Type {3,2,4,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,24}*1152d
if this polytope has a name.
Group : SmallGroup(1152,155800)
Rank : 5
Schlafli Type : {3,2,4,24}
Number of vertices, edges, etc : 3, 3, 4, 48, 24
Order of s₀s₁s₂s₃s₄ : 24
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {3,2,4,12}*576b
   4-fold quotients : {3,2,4,6}*288c
   8-fold quotients : {3,2,4,3}*144
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4,17)( 5,16)( 6,19)( 7,18)( 8,21)( 9,20)(10,23)(11,22)(12,25)(13,24)
(14,27)(15,26)(28,41)(29,40)(30,43)(31,42)(32,45)(33,44)(34,47)(35,46)(36,49)
(37,48)(38,51)(39,50)(52,65)(53,64)(54,67)(55,66)(56,69)(57,68)(58,71)(59,70)
(60,73)(61,72)(62,75)(63,74)(76,89)(77,88)(78,91)(79,90)(80,93)(81,92)(82,95)
(83,94)(84,97)(85,96)(86,99)(87,98);;
s3 := ( 5, 6)( 8,12)( 9,14)(10,13)(11,15)(17,18)(20,24)(21,26)(22,25)(23,27)
(28,40)(29,42)(30,41)(31,43)(32,48)(33,50)(34,49)(35,51)(36,44)(37,46)(38,45)
(39,47)(52,76)(53,78)(54,77)(55,79)(56,84)(57,86)(58,85)(59,87)(60,80)(61,82)
(62,81)(63,83)(64,88)(65,90)(66,89)(67,91)(68,96)(69,98)(70,97)(71,99)(72,92)
(73,94)(74,93)(75,95);;
s4 := ( 4,56)( 5,57)( 6,59)( 7,58)( 8,52)( 9,53)(10,55)(11,54)(12,60)(13,61)
(14,63)(15,62)(16,68)(17,69)(18,71)(19,70)(20,64)(21,65)(22,67)(23,66)(24,72)
(25,73)(26,75)(27,74)(28,92)(29,93)(30,95)(31,94)(32,88)(33,89)(34,91)(35,90)
(36,96)(37,97)(38,99)(39,98)(40,80)(41,81)(42,83)(43,82)(44,76)(45,77)(46,79)
(47,78)(48,84)(49,85)(50,87)(51,86);;
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s4*s3*s4*s3*s4*s3*s4*s3*s2*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(99)!(2,3);
s1 := Sym(99)!(1,2);
s2 := Sym(99)!( 4,17)( 5,16)( 6,19)( 7,18)( 8,21)( 9,20)(10,23)(11,22)(12,25)
(13,24)(14,27)(15,26)(28,41)(29,40)(30,43)(31,42)(32,45)(33,44)(34,47)(35,46)
(36,49)(37,48)(38,51)(39,50)(52,65)(53,64)(54,67)(55,66)(56,69)(57,68)(58,71)
(59,70)(60,73)(61,72)(62,75)(63,74)(76,89)(77,88)(78,91)(79,90)(80,93)(81,92)
(82,95)(83,94)(84,97)(85,96)(86,99)(87,98);
s3 := Sym(99)!( 5, 6)( 8,12)( 9,14)(10,13)(11,15)(17,18)(20,24)(21,26)(22,25)
(23,27)(28,40)(29,42)(30,41)(31,43)(32,48)(33,50)(34,49)(35,51)(36,44)(37,46)
(38,45)(39,47)(52,76)(53,78)(54,77)(55,79)(56,84)(57,86)(58,85)(59,87)(60,80)
(61,82)(62,81)(63,83)(64,88)(65,90)(66,89)(67,91)(68,96)(69,98)(70,97)(71,99)
(72,92)(73,94)(74,93)(75,95);
s4 := Sym(99)!( 4,56)( 5,57)( 6,59)( 7,58)( 8,52)( 9,53)(10,55)(11,54)(12,60)
(13,61)(14,63)(15,62)(16,68)(17,69)(18,71)(19,70)(20,64)(21,65)(22,67)(23,66)
(24,72)(25,73)(26,75)(27,74)(28,92)(29,93)(30,95)(31,94)(32,88)(33,89)(34,91)
(35,90)(36,96)(37,97)(38,99)(39,98)(40,80)(41,81)(42,83)(43,82)(44,76)(45,77)
(46,79)(47,78)(48,84)(49,85)(50,87)(51,86);
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s4*s3*s4*s3*s4*s3*s4*s3*s2*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s2 >;

to this polytope