Polytope of Type {2,10,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,4,6}*1440
if this polytope has a name.
Group : SmallGroup(1440,5890)
Rank : 5
Schlafli Type : {2,10,4,6}
Number of vertices, edges, etc : 2, 10, 30, 18, 9
Order of s₀s₁s₂s₃s₄ : 20
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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) :
   5-fold quotients : {2,2,4,6}*288
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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