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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,12,2,5}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240141)
Rank : 6
Schlafli Type : {2,4,12,2,5}
Number of vertices, edges, etc : 2, 4, 24, 12, 5, 5
Order of s₀s₁s₂s₃s₄s₅ : 60
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {2,4,6,2,5}*960c
   4-fold quotients : {2,4,3,2,5}*480
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 3,23)( 4,15)( 5,12)( 6,37)( 7,38)( 8, 9)(10,29)(11,30)(13,24)(14,25)
(16,21)(17,22)(18,49)(19,50)(20,48)(26,44)(27,46)(28,42)(31,47)(32,45)(33,43)
(34,41)(35,39)(36,40);;
s2 := ( 4, 5)( 6, 7)( 8,18)(10,14)(11,13)(12,26)(15,31)(16,34)(17,19)(20,36)
(21,22)(23,39)(24,42)(25,32)(27,30)(28,46)(29,43)(33,45)(37,48)(38,40)(41,50)
(44,47);;
s3 := ( 3,11)( 4, 7)( 5,22)( 6,10)( 8,25)( 9,14)(12,17)(13,21)(15,38)(16,24)
(18,28)(19,45)(20,31)(23,30)(26,41)(27,36)(29,37)(32,50)(33,39)(34,44)(35,43)
(40,46)(42,49)(47,48);;
s4 := (52,53)(54,55);;
s5 := (51,52)(53,54);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s1*s2*s1*s2*s1*s2*s1*s2, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(55)!(1,2);
s1 := Sym(55)!( 3,23)( 4,15)( 5,12)( 6,37)( 7,38)( 8, 9)(10,29)(11,30)(13,24)
(14,25)(16,21)(17,22)(18,49)(19,50)(20,48)(26,44)(27,46)(28,42)(31,47)(32,45)
(33,43)(34,41)(35,39)(36,40);
s2 := Sym(55)!( 4, 5)( 6, 7)( 8,18)(10,14)(11,13)(12,26)(15,31)(16,34)(17,19)
(20,36)(21,22)(23,39)(24,42)(25,32)(27,30)(28,46)(29,43)(33,45)(37,48)(38,40)
(41,50)(44,47);
s3 := Sym(55)!( 3,11)( 4, 7)( 5,22)( 6,10)( 8,25)( 9,14)(12,17)(13,21)(15,38)
(16,24)(18,28)(19,45)(20,31)(23,30)(26,41)(27,36)(29,37)(32,50)(33,39)(34,44)
(35,43)(40,46)(42,49)(47,48);
s4 := Sym(55)!(52,53)(54,55);
s5 := Sym(55)!(51,52)(53,54);
poly := sub<Sym(55)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s1*s2*s1*s2*s1*s2*s1*s2, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s2 >;

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