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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,8,6,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,235343)
Rank : 6
Schlafli Type : {5,2,8,6,2}
Number of vertices, edges, etc : 5, 5, 8, 24, 6, 2
Order of s₀s₁s₂s₃s₄s₅ : 120
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,4,6,2}*960a
   3-fold quotients : {5,2,8,2,2}*640
   4-fold quotients : {5,2,2,6,2}*480
   6-fold quotients : {5,2,4,2,2}*320
   8-fold quotients : {5,2,2,3,2}*240
   12-fold quotients : {5,2,2,2,2}*160
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7,10)(11,14)(12,15)(13,16)(17,20)(18,21)(19,22)(23,26)(24,27);;
s3 := ( 6, 7)( 8,12)( 9,11)(10,13)(14,18)(15,17)(16,19)(20,24)(21,23)(22,25)
(26,29)(27,28);;
s4 := ( 6, 8)( 7,11)(10,14)(13,17)(16,20)(19,23)(22,26)(25,28);;
s5 := (30,31);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s2*s3*s4*s3*s2*s3*s4*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(31)!(2,3)(4,5);
s1 := Sym(31)!(1,2)(3,4);
s2 := Sym(31)!( 7,10)(11,14)(12,15)(13,16)(17,20)(18,21)(19,22)(23,26)(24,27);
s3 := Sym(31)!( 6, 7)( 8,12)( 9,11)(10,13)(14,18)(15,17)(16,19)(20,24)(21,23)
(22,25)(26,29)(27,28);
s4 := Sym(31)!( 6, 8)( 7,11)(10,14)(13,17)(16,20)(19,23)(22,26)(25,28);
s5 := Sym(31)!(30,31);
poly := sub<Sym(31)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s2*s3*s4*s3*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope