Polytope of Type {4,4,2,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,2,12}*768
if this polytope has a name.
Group : SmallGroup(768,364861)
Rank : 5
Schlafli Type : {4,4,2,12}
Number of vertices, edges, etc : 4, 8, 4, 12, 12
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {2,4,2,12}*384, {4,2,2,12}*384, {4,4,2,6}*384
   3-fold quotients : {4,4,2,4}*256
   4-fold quotients : {4,4,2,3}*192, {2,2,2,12}*192, {2,4,2,6}*192, {4,2,2,6}*192
   6-fold quotients : {4,4,2,2}*128, {2,4,2,4}*128, {4,2,2,4}*128
   8-fold quotients : {2,4,2,3}*96, {4,2,2,3}*96, {2,2,2,6}*96
   12-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64, {4,2,2,2}*64
   16-fold quotients : {2,2,2,3}*48
   24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3)(4,6);;
s1 := (1,2)(3,5)(4,7)(6,8);;
s2 := (2,4)(3,6);;
s3 := (10,11)(12,13)(15,18)(16,17)(19,20);;
s4 := ( 9,15)(10,12)(11,19)(13,16)(14,17)(18,20);;
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, 
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*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(20)!(2,3)(4,6);
s1 := Sym(20)!(1,2)(3,5)(4,7)(6,8);
s2 := Sym(20)!(2,4)(3,6);
s3 := Sym(20)!(10,11)(12,13)(15,18)(16,17)(19,20);
s4 := Sym(20)!( 9,15)(10,12)(11,19)(13,16)(14,17)(18,20);
poly := sub<Sym(20)|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, 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*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope