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

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

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

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