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Polytope of Type {2,5,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,8}*960
if this polytope has a name.
Group : SmallGroup(960,10869)
Rank : 4
Schlafli Type : {2,5,8}
Number of vertices, edges, etc : 2, 30, 120, 48
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,5,8,2} of size 1920
Vertex Figure Of :
   {2,2,5,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,5,4}*480
   4-fold quotients : {2,5,4}*240
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,10,8}*1920c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope