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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,24,2}*768d
if this polytope has a name.
Group : SmallGroup(768,1089134)
Rank : 5
Schlafli Type : {2,4,24,2}
Number of vertices, edges, etc : 2, 4, 48, 24, 2
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 : {2,4,12,2}*384b
   4-fold quotients : {2,4,6,2}*192c
   8-fold quotients : {2,4,3,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 3,16)( 4,15)( 5,18)( 6,17)( 7,20)( 8,19)( 9,22)(10,21)(11,24)(12,23)
(13,26)(14,25)(27,40)(28,39)(29,42)(30,41)(31,44)(32,43)(33,46)(34,45)(35,48)
(36,47)(37,50)(38,49)(51,64)(52,63)(53,66)(54,65)(55,68)(56,67)(57,70)(58,69)
(59,72)(60,71)(61,74)(62,73)(75,88)(76,87)(77,90)(78,89)(79,92)(80,91)(81,94)
(82,93)(83,96)(84,95)(85,98)(86,97);;
s2 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)(22,26)
(27,39)(28,41)(29,40)(30,42)(31,47)(32,49)(33,48)(34,50)(35,43)(36,45)(37,44)
(38,46)(51,75)(52,77)(53,76)(54,78)(55,83)(56,85)(57,84)(58,86)(59,79)(60,81)
(61,80)(62,82)(63,87)(64,89)(65,88)(66,90)(67,95)(68,97)(69,96)(70,98)(71,91)
(72,93)(73,92)(74,94);;
s3 := ( 3,55)( 4,56)( 5,58)( 6,57)( 7,51)( 8,52)( 9,54)(10,53)(11,59)(12,60)
(13,62)(14,61)(15,67)(16,68)(17,70)(18,69)(19,63)(20,64)(21,66)(22,65)(23,71)
(24,72)(25,74)(26,73)(27,91)(28,92)(29,94)(30,93)(31,87)(32,88)(33,90)(34,89)
(35,95)(36,96)(37,98)(38,97)(39,79)(40,80)(41,82)(42,81)(43,75)(44,76)(45,78)
(46,77)(47,83)(48,84)(49,86)(50,85);;
s4 := ( 99,100);;
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*s1*s0*s1, 
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(100)!(1,2);
s1 := Sym(100)!( 3,16)( 4,15)( 5,18)( 6,17)( 7,20)( 8,19)( 9,22)(10,21)(11,24)
(12,23)(13,26)(14,25)(27,40)(28,39)(29,42)(30,41)(31,44)(32,43)(33,46)(34,45)
(35,48)(36,47)(37,50)(38,49)(51,64)(52,63)(53,66)(54,65)(55,68)(56,67)(57,70)
(58,69)(59,72)(60,71)(61,74)(62,73)(75,88)(76,87)(77,90)(78,89)(79,92)(80,91)
(81,94)(82,93)(83,96)(84,95)(85,98)(86,97);
s2 := Sym(100)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)
(22,26)(27,39)(28,41)(29,40)(30,42)(31,47)(32,49)(33,48)(34,50)(35,43)(36,45)
(37,44)(38,46)(51,75)(52,77)(53,76)(54,78)(55,83)(56,85)(57,84)(58,86)(59,79)
(60,81)(61,80)(62,82)(63,87)(64,89)(65,88)(66,90)(67,95)(68,97)(69,96)(70,98)
(71,91)(72,93)(73,92)(74,94);
s3 := Sym(100)!( 3,55)( 4,56)( 5,58)( 6,57)( 7,51)( 8,52)( 9,54)(10,53)(11,59)
(12,60)(13,62)(14,61)(15,67)(16,68)(17,70)(18,69)(19,63)(20,64)(21,66)(22,65)
(23,71)(24,72)(25,74)(26,73)(27,91)(28,92)(29,94)(30,93)(31,87)(32,88)(33,90)
(34,89)(35,95)(36,96)(37,98)(38,97)(39,79)(40,80)(41,82)(42,81)(43,75)(44,76)
(45,78)(46,77)(47,83)(48,84)(49,86)(50,85);
s4 := Sym(100)!( 99,100);
poly := sub<Sym(100)|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*s1*s0*s1, 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, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s3*s2*s3*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s1 >;

to this polytope