Polytope of Type {8,10,2}

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

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

Permutation Representation (Magma) :

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

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