Polytope of Type {10,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,8,2}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240976)
Rank : 4
Schlafli Type : {10,8,2}
Number of vertices, edges, etc : 60, 240, 48, 2
Order of s₀s₁s₂s₃ : 12
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 : {10,4,2}*960c
   4-fold quotients : {5,4,2}*480, {10,4,2}*480a, {10,4,2}*480b
   8-fold quotients : {5,4,2}*240
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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