Polytope of Type {5,2,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,12,4}*960c
if this polytope has a name.
Group : SmallGroup(960,10951)
Rank : 5
Schlafli Type : {5,2,12,4}
Number of vertices, edges, etc : 5, 5, 12, 24, 4
Order of s₀s₁s₂s₃s₄ : 60
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,12,4,2} of size 1920
Vertex Figure Of :
   {2,5,2,12,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,6,4}*480c
   4-fold quotients : {5,2,3,4}*240
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,12,4}*1920b, {10,2,12,4}*1920c
Permutation Representation (GAP) :

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

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