Polytope of Type {6,16,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,16,2,5}*1920
if this polytope has a name.
Group : SmallGroup(1920,203901)
Rank : 5
Schlafli Type : {6,16,2,5}
Number of vertices, edges, etc : 6, 48, 16, 5, 5
Order of s₀s₁s₂s₃s₄ : 240
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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) :
   2-fold quotients : {6,8,2,5}*960
   3-fold quotients : {2,16,2,5}*640
   4-fold quotients : {6,4,2,5}*480a
   6-fold quotients : {2,8,2,5}*320
   8-fold quotients : {6,2,2,5}*240
   12-fold quotients : {2,4,2,5}*160
   16-fold quotients : {3,2,2,5}*120
   24-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)
(32,33)(35,36)(38,39)(41,42)(44,45)(47,48);;
s1 := ( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,20)(14,19)(15,21)(16,23)(17,22)
(18,24)(25,44)(26,43)(27,45)(28,47)(29,46)(30,48)(31,38)(32,37)(33,39)(34,41)
(35,40)(36,42);;
s2 := ( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,34)( 8,35)( 9,36)(10,31)
(11,32)(12,33)(13,43)(14,44)(15,45)(16,46)(17,47)(18,48)(19,37)(20,38)(21,39)
(22,40)(23,41)(24,42);;
s3 := (50,51)(52,53);;
s4 := (49,50)(51,52);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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(53)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)
(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48);
s1 := Sym(53)!( 1, 2)( 4, 5)( 7,11)( 8,10)( 9,12)(13,20)(14,19)(15,21)(16,23)
(17,22)(18,24)(25,44)(26,43)(27,45)(28,47)(29,46)(30,48)(31,38)(32,37)(33,39)
(34,41)(35,40)(36,42);
s2 := Sym(53)!( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,34)( 8,35)( 9,36)
(10,31)(11,32)(12,33)(13,43)(14,44)(15,45)(16,46)(17,47)(18,48)(19,37)(20,38)
(21,39)(22,40)(23,41)(24,42);
s3 := Sym(53)!(50,51)(52,53);
s4 := Sym(53)!(49,50)(51,52);
poly := sub<Sym(53)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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 >;

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