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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,12,3}*960
if this polytope has a name.
Group : SmallGroup(960,10979)
Rank : 5
Schlafli Type : {5,2,12,3}
Number of vertices, edges, etc : 5, 5, 16, 24, 4
Order of s₀s₁s₂s₃s₄ : 40
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,12,3,2} of size 1920
Vertex Figure Of :
   {2,5,2,12,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,6,3}*480
   4-fold quotients : {5,2,3,3}*240
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,12,6}*1920b, {10,2,12,3}*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 := ( 6,14)( 7, 9)( 8,30)(10,15)(11,53)(12,52)(13,18)(16,47)(17,46)(19,31)
(20,51)(21,49)(22,41)(23,38)(24,37)(25,39)(26,35)(27,40)(28,36)(29,34)(32,45)
(33,44)(42,48)(43,50);;
s4 := ( 6,51)( 7,45)( 8,44)( 9,41)(10,53)(11,16)(12,17)(13,49)(14,29)(15,47)
(18,26)(19,46)(20,34)(21,35)(22,32)(23,33)(24,36)(25,50)(27,39)(28,48)(30,38)
(31,52)(37,42)(40,43);;
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, 
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s2*s3*s2*s3*s4*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)(11,24)(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)!( 6,14)( 7, 9)( 8,30)(10,15)(11,53)(12,52)(13,18)(16,47)(17,46)
(19,31)(20,51)(21,49)(22,41)(23,38)(24,37)(25,39)(26,35)(27,40)(28,36)(29,34)
(32,45)(33,44)(42,48)(43,50);
s4 := Sym(53)!( 6,51)( 7,45)( 8,44)( 9,41)(10,53)(11,16)(12,17)(13,49)(14,29)
(15,47)(18,26)(19,46)(20,34)(21,35)(22,32)(23,33)(24,36)(25,50)(27,39)(28,48)
(30,38)(31,52)(37,42)(40,43);
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, s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s4*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3 >;

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