Polytope of Type {8,2,2,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,2,3,2}*384
if this polytope has a name.
Group : SmallGroup(384,19745)
Rank : 6
Schlafli Type : {8,2,2,3,2}
Number of vertices, edges, etc : 8, 8, 2, 3, 3, 2
Order of s₀s₁s₂s₃s₄s₅ : 24
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,2,2,3,2,2} of size 768
   {8,2,2,3,2,3} of size 1152
   {8,2,2,3,2,5} of size 1920
Vertex Figure Of :
   {2,8,2,2,3,2} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,2,3,2}*192
   4-fold quotients : {2,2,2,3,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,4,2,3,2}*768a, {16,2,2,3,2}*768, {8,2,2,6,2}*768
   3-fold covers : {8,2,2,9,2}*1152, {8,2,2,3,6}*1152, {8,2,6,3,2}*1152, {8,6,2,3,2}*1152, {24,2,2,3,2}*1152
   5-fold covers : {8,2,2,15,2}*1920, {8,10,2,3,2}*1920, {40,2,2,3,2}*1920
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := ( 9,10);;
s3 := (12,13);;
s4 := (11,12);;
s5 := (14,15);;
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, s2*s3*s2*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, s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(15)!(2,3)(4,5)(6,7);
s1 := Sym(15)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(15)!( 9,10);
s3 := Sym(15)!(12,13);
s4 := Sym(15)!(11,12);
s5 := Sym(15)!(14,15);
poly := sub<Sym(15)|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, s2*s3*s2*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, s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope