Polytope of Type {2,3,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,24}*1152
if this polytope has a name.
Group : SmallGroup(1152,155485)
Rank : 4
Schlafli Type : {2,3,24}
Number of vertices, edges, etc : 2, 12, 144, 96
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 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) :
   3-fold quotients : {2,3,8}*384
   4-fold quotients : {2,3,12}*288
   12-fold quotients : {2,3,4}*96
   16-fold quotients : {2,3,6}*72
   24-fold quotients : {2,3,4}*48
   48-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 5, 6)( 7,14)( 8,13)( 9,11)(10,12)(15,16)(19,35)(20,36)(21,38)(22,37)
(23,46)(24,45)(25,43)(26,44)(27,41)(28,42)(29,40)(30,39)(31,48)(32,47)(33,49)
(34,50);;
s2 := ( 3,19)( 4,21)( 5,20)( 6,22)( 7,26)( 8,24)( 9,25)(10,23)(11,34)(12,32)
(13,33)(14,31)(15,30)(16,28)(17,29)(18,27)(36,37)(39,42)(43,50)(44,48)(45,49)
(46,47);;
s3 := ( 3,17)( 4,18)( 5,15)( 6,16)( 7,13)( 8,14)( 9,11)(10,12)(19,49)(20,50)
(21,47)(22,48)(23,45)(24,46)(25,43)(26,44)(27,41)(28,42)(29,39)(30,40)(31,37)
(32,38)(33,35)(34,36);;
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*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 5, 6)( 7,14)( 8,13)( 9,11)(10,12)(15,16)(19,35)(20,36)(21,38)
(22,37)(23,46)(24,45)(25,43)(26,44)(27,41)(28,42)(29,40)(30,39)(31,48)(32,47)
(33,49)(34,50);
s2 := Sym(50)!( 3,19)( 4,21)( 5,20)( 6,22)( 7,26)( 8,24)( 9,25)(10,23)(11,34)
(12,32)(13,33)(14,31)(15,30)(16,28)(17,29)(18,27)(36,37)(39,42)(43,50)(44,48)
(45,49)(46,47);
s3 := Sym(50)!( 3,17)( 4,18)( 5,15)( 6,16)( 7,13)( 8,14)( 9,11)(10,12)(19,49)
(20,50)(21,47)(22,48)(23,45)(24,46)(25,43)(26,44)(27,41)(28,42)(29,39)(30,40)
(31,37)(32,38)(33,35)(34,36);
poly := sub<Sym(50)|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*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2 >;

to this polytope