Polytope of Type {2,6,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,10}*960a
if this polytope has a name.
Group : SmallGroup(960,10869)
Rank : 4
Schlafli Type : {2,6,10}
Number of vertices, edges, etc : 2, 24, 120, 40
Order of s₀s₁s₂s₃ : 8
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,10,2} of size 1920
Vertex Figure Of :
   {2,2,6,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,5}*480a
   4-fold quotients : {2,6,5}*240a
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,6,10}*1920e, {2,6,10}*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 := ( 3,18)( 4,10)( 5,35)( 6,34)( 7,17)( 8, 9)(11,36)(12,33)(13,30)(14,29)
(15,21)(16,20)(19,38)(26,41)(27,42)(28,37)(31,39)(32,40);;
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*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s3*s2*s1*s2 ];;
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)!( 3,18)( 4,10)( 5,35)( 6,34)( 7,17)( 8, 9)(11,36)(12,33)(13,30)
(14,29)(15,21)(16,20)(19,38)(26,41)(27,42)(28,37)(31,39)(32,40);
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*s1*s2*s3*s1*s2*s1*s2*s3*s2*s3*s2*s3*s2*s1*s2 >;

to this polytope