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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,16,6}*1920
if this polytope has a name.
Group : SmallGroup(1920,203901)
Rank : 5
Schlafli Type : {5,2,16,6}
Number of vertices, edges, etc : 5, 5, 16, 48, 6
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 : {5,2,8,6}*960
   3-fold quotients : {5,2,16,2}*640
   4-fold quotients : {5,2,4,6}*480a
   6-fold quotients : {5,2,8,2}*320
   8-fold quotients : {5,2,2,6}*240
   12-fold quotients : {5,2,4,2}*160
   16-fold quotients : {5,2,2,3}*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 := (12,15)(13,16)(14,17)(18,24)(19,25)(20,26)(21,27)(22,28)(23,29)(30,48)
(31,49)(32,50)(33,51)(34,52)(35,53)(36,42)(37,43)(38,44)(39,45)(40,46)
(41,47);;
s3 := ( 6,30)( 7,32)( 8,31)( 9,33)(10,35)(11,34)(12,39)(13,41)(14,40)(15,36)
(16,38)(17,37)(18,48)(19,50)(20,49)(21,51)(22,53)(23,52)(24,42)(25,44)(26,43)
(27,45)(28,47)(29,46);;
s4 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)
(36,37)(39,40)(42,43)(45,46)(48,49)(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, 
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, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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)!(12,15)(13,16)(14,17)(18,24)(19,25)(20,26)(21,27)(22,28)(23,29)
(30,48)(31,49)(32,50)(33,51)(34,52)(35,53)(36,42)(37,43)(38,44)(39,45)(40,46)
(41,47);
s3 := Sym(53)!( 6,30)( 7,32)( 8,31)( 9,33)(10,35)(11,34)(12,39)(13,41)(14,40)
(15,36)(16,38)(17,37)(18,48)(19,50)(20,49)(21,51)(22,53)(23,52)(24,42)(25,44)
(26,43)(27,45)(28,47)(29,46);
s4 := Sym(53)!( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)
(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(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, 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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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 >;

to this polytope