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Polytope of Type {2,10,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,8}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240973)
Rank : 4
Schlafli Type : {2,10,8}
Number of vertices, edges, etc : 2, 60, 240, 48
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,5,8}*960, {2,10,4}*960c
   4-fold quotients : {2,5,4}*480, {2,10,4}*480a, {2,10,4}*480b
   8-fold quotients : {2,5,4}*240
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

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