Polytope of Type {2,6,8}

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

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

Permutation Representation (Magma) :

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

to this polytope