Polytope of Type {4,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,2}*144
if this polytope has a name.
Group : SmallGroup(144,186)
Rank : 4
Schlafli Type : {4,4,2}
Number of vertices, edges, etc : 9, 18, 9, 2
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,4,2,2} of size 288
   {4,4,2,3} of size 432
   {4,4,2,4} of size 576
   {4,4,2,5} of size 720
   {4,4,2,6} of size 864
   {4,4,2,7} of size 1008
   {4,4,2,8} of size 1152
   {4,4,2,9} of size 1296
   {4,4,2,10} of size 1440
   {4,4,2,11} of size 1584
   {4,4,2,12} of size 1728
   {4,4,2,13} of size 1872
Vertex Figure Of :
   {2,4,4,2} of size 288
   {3,4,4,2} of size 1440
   {4,4,4,2} of size 1440
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,2}*288
   3-fold covers : {4,12,2}*432, {12,4,2}*432
   4-fold covers : {4,4,4}*576a, {4,4,2}*576
   6-fold covers : {4,12,2}*864a, {12,4,2}*864a, {4,4,6}*864b, {4,12,2}*864b, {12,4,2}*864b
   8-fold covers : {4,4,4}*1152b, {4,8,2}*1152a, {8,4,2}*1152a, {4,8,2}*1152b, {8,4,2}*1152b, {4,4,2}*1152, {4,4,8}*1152
   9-fold covers : {4,4,2}*1296, {12,12,2}*1296, {4,4,6}*1296
   10-fold covers : {4,4,10}*1440, {4,20,2}*1440, {20,4,2}*1440
   12-fold covers : {4,12,4}*1728b, {12,4,4}*1728a, {4,12,2}*1728a, {12,4,2}*1728a, {4,4,12}*1728b, {4,12,2}*1728d, {12,4,2}*1728c, {4,4,6}*1728b, {4,12,4}*1728c, {12,4,4}*1728c, {12,12,2}*1728m
Permutation Representation (GAP) :

s0 := (5,6);;
s1 := (1,2)(3,5)(4,6);;
s2 := (2,3);;
s3 := (7,8);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(8)!(5,6);
s1 := Sym(8)!(1,2)(3,5)(4,6);
s2 := Sym(8)!(2,3);
s3 := Sym(8)!(7,8);
poly := sub<Sym(8)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;

to this polytope