Polytope of Type {8,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,2}*960b
if this polytope has a name.
Group : SmallGroup(960,10869)
Rank : 4
Schlafli Type : {8,6,2}
Number of vertices, edges, etc : 40, 120, 30, 2
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,6,2,2} of size 1920
Vertex Figure Of :
   {2,8,6,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6,2}*480c
   4-fold quotients : {4,6,2}*240
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,6,2}*1920a
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope