Polytope of Type {2,2,6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,8}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240973)
Rank : 5
Schlafli Type : {2,2,6,8}
Number of vertices, edges, etc : 2, 2, 30, 120, 40
Order of s₀s₁s₂s₃s₄ : 10
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) :
   2-fold quotients : {2,2,6,4}*960c
   4-fold quotients : {2,2,6,4}*480
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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