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

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

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

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