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Polytope of Type {2,6,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,24}*1152a
if this polytope has a name.
Group : SmallGroup(1152,155485)
Rank : 4
Schlafli Type : {2,6,24}
Number of vertices, edges, etc : 2, 12, 144, 48
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 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) :
   3-fold quotients : {2,6,8}*384a
   4-fold quotients : {2,6,12}*288d
   12-fold quotients : {2,6,4}*96b
   24-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 7,12)( 8,11)( 9,13)(10,14)(17,18)(21,22)(23,28)(24,27)(25,29)
(26,30)(33,34)(37,38)(39,44)(40,43)(41,45)(42,46)(49,50);;
s2 := ( 4, 5)( 7,10)(11,18)(12,16)(13,17)(14,15)(19,35)(20,37)(21,36)(22,38)
(23,42)(24,40)(25,41)(26,39)(27,50)(28,48)(29,49)(30,47)(31,46)(32,44)(33,45)
(34,43);;
s3 := ( 3,31)( 4,32)( 5,33)( 6,34)( 7,27)( 8,28)( 9,29)(10,30)(11,23)(12,24)
(13,25)(14,26)(15,19)(16,20)(17,21)(18,22)(35,47)(36,48)(37,49)(38,50)(39,43)
(40,44)(41,45)(42,46);;
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*s1*s2*s3*s1*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 5, 6)( 7,12)( 8,11)( 9,13)(10,14)(17,18)(21,22)(23,28)(24,27)
(25,29)(26,30)(33,34)(37,38)(39,44)(40,43)(41,45)(42,46)(49,50);
s2 := Sym(50)!( 4, 5)( 7,10)(11,18)(12,16)(13,17)(14,15)(19,35)(20,37)(21,36)
(22,38)(23,42)(24,40)(25,41)(26,39)(27,50)(28,48)(29,49)(30,47)(31,46)(32,44)
(33,45)(34,43);
s3 := Sym(50)!( 3,31)( 4,32)( 5,33)( 6,34)( 7,27)( 8,28)( 9,29)(10,30)(11,23)
(12,24)(13,25)(14,26)(15,19)(16,20)(17,21)(18,22)(35,47)(36,48)(37,49)(38,50)
(39,43)(40,44)(41,45)(42,46);
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*s3*s1*s2*s3*s1*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >; 
 

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