Polytope of Type {5,8,2}

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

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

Permutation Representation (Magma) :

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

to this polytope