Polytope of Type {5,2,3,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,3,12}*960
if this polytope has a name.
Group : SmallGroup(960,10979)
Rank : 5
Schlafli Type : {5,2,3,12}
Number of vertices, edges, etc : 5, 5, 4, 24, 16
Order of s₀s₁s₂s₃s₄ : 40
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,3,12,2} of size 1920
Vertex Figure Of :
   {2,5,2,3,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,3,6}*480
   4-fold quotients : {5,2,3,3}*240
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,6,12}*1920b, {10,2,3,12}*1920
Permutation Representation (GAP) :

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

to this polytope