Polytope of Type {5,2,6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,6,8}*960
if this polytope has a name.
Group : SmallGroup(960,8239)
Rank : 5
Schlafli Type : {5,2,6,8}
Number of vertices, edges, etc : 5, 5, 6, 24, 8
Order of s₀s₁s₂s₃s₄ : 120
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,6,8,2} of size 1920
Vertex Figure Of :
   {2,5,2,6,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,6,4}*480a
   3-fold quotients : {5,2,2,8}*320
   4-fold quotients : {5,2,6,2}*240
   6-fold quotients : {5,2,2,4}*160
   8-fold quotients : {5,2,3,2}*120
   12-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,12,8}*1920a, {5,2,6,16}*1920, {10,2,6,8}*1920
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(28,29);;
s3 := ( 6, 8)( 7,14)(10,11)(12,15)(13,20)(16,17)(18,21)(19,26)(22,23)(24,27)
(25,28);;
s4 := ( 6, 7)( 8,11)( 9,12)(10,13)(14,17)(15,18)(16,19)(20,23)(21,24)(22,25)
(26,28)(27,29);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(29)!(2,3)(4,5);
s1 := Sym(29)!(1,2)(3,4);
s2 := Sym(29)!( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(28,29);
s3 := Sym(29)!( 6, 8)( 7,14)(10,11)(12,15)(13,20)(16,17)(18,21)(19,26)(22,23)
(24,27)(25,28);
s4 := Sym(29)!( 6, 7)( 8,11)( 9,12)(10,13)(14,17)(15,18)(16,19)(20,23)(21,24)
(22,25)(26,28)(27,29);
poly := sub<Sym(29)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope