Polytope of Type {6,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8,2}*960a
if this polytope has a name.
Group : SmallGroup(960,10869)
Rank : 4
Schlafli Type : {6,8,2}
Number of vertices, edges, etc : 30, 120, 40, 2
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,8,2,2} of size 1920
Vertex Figure Of :
   {2,6,8,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4,2}*480c
   4-fold quotients : {6,4,2}*240
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,8,2}*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 := ( 3,10)( 4, 9)( 7,26)( 8,17)(11,22)(12,23)(13,16)(14,15)(18,37)(19,38)
(20,25)(21,24)(27,32)(28,31)(29,36)(30,35)(33,40)(34,39);;
s2 := ( 1,18)( 2,35)( 3,29)( 4,30)( 5,19)( 6,36)( 7,16)( 9,38)(10,37)(11,17)
(12,13)(14,25)(20,22)(24,26)(28,40)(31,34)(32,33);;
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, 
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*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1*s2 ];;
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)!( 3,10)( 4, 9)( 7,26)( 8,17)(11,22)(12,23)(13,16)(14,15)(18,37)
(19,38)(20,25)(21,24)(27,32)(28,31)(29,36)(30,35)(33,40)(34,39);
s2 := Sym(42)!( 1,18)( 2,35)( 3,29)( 4,30)( 5,19)( 6,36)( 7,16)( 9,38)(10,37)
(11,17)(12,13)(14,25)(20,22)(24,26)(28,40)(31,34)(32,33);
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, 
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*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s2*s1*s2 >;

to this polytope