Polytope of Type {5,2,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,48}*960
if this polytope has a name.
Group : SmallGroup(960,1009)
Rank : 4
Schlafli Type : {5,2,48}
Number of vertices, edges, etc : 5, 5, 48, 48
Order of s₀s₁s₂s₃ : 240
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,48,2} of size 1920
Vertex Figure Of :
   {2,5,2,48} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,24}*480
   3-fold quotients : {5,2,16}*320
   4-fold quotients : {5,2,12}*240
   6-fold quotients : {5,2,8}*160
   8-fold quotients : {5,2,6}*120
   12-fold quotients : {5,2,4}*80
   16-fold quotients : {5,2,3}*60
   24-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,96}*1920, {10,2,48}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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