Polytope of Type {3,2,4,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,3}*144
if this polytope has a name.
Group : SmallGroup(144,183)
Rank : 5
Schlafli Type : {3,2,4,3}
Number of vertices, edges, etc : 3, 3, 4, 6, 3
Order of s₀s₁s₂s₃s₄ : 3
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,4,3,2} of size 288
   {3,2,4,3,4} of size 576
   {3,2,4,3,6} of size 864
   {3,2,4,3,4} of size 1152
Vertex Figure Of :
   {2,3,2,4,3} of size 288
   {3,3,2,4,3} of size 576
   {4,3,2,4,3} of size 576
   {6,3,2,4,3} of size 864
   {4,3,2,4,3} of size 1152
   {6,3,2,4,3} of size 1152
   {5,3,2,4,3} of size 1440
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,4,3}*288, {3,2,4,6}*288b, {3,2,4,6}*288c, {6,2,4,3}*288
   3-fold covers : {9,2,4,3}*432, {3,2,4,9}*432
   4-fold covers : {3,2,4,12}*576b, {3,2,4,12}*576c, {12,2,4,3}*576, {3,2,8,3}*576, {3,2,4,6}*576, {6,2,4,3}*576, {6,2,4,6}*576b, {6,2,4,6}*576c
   5-fold covers : {3,2,4,15}*720, {15,2,4,3}*720
   6-fold covers : {9,2,4,3}*864, {9,2,4,6}*864b, {9,2,4,6}*864c, {18,2,4,3}*864, {3,2,4,9}*864, {3,2,4,18}*864b, {3,2,4,18}*864c, {6,2,4,9}*864, {3,6,4,3}*864, {3,2,12,3}*864, {3,2,12,6}*864d
   7-fold covers : {3,2,4,21}*1008, {21,2,4,3}*1008
   8-fold covers : {3,2,4,6}*1152a, {6,4,4,3}*1152a, {3,2,8,3}*1152, {3,2,8,6}*1152a, {3,2,4,24}*1152c, {3,2,4,24}*1152d, {24,2,4,3}*1152, {3,2,4,12}*1152b, {6,2,4,12}*1152b, {6,2,4,12}*1152c, {12,2,4,3}*1152, {12,2,4,6}*1152b, {12,2,4,6}*1152c, {3,2,4,6}*1152b, {3,2,4,12}*1152c, {6,4,4,3}*1152b, {3,2,8,6}*1152b, {6,2,8,3}*1152, {3,2,8,6}*1152c, {3,4,4,3}*1152, {6,2,4,6}*1152
   9-fold covers : {27,2,4,3}*1296, {3,2,4,27}*1296, {9,2,4,9}*1296
   10-fold covers : {3,2,20,6}*1440b, {3,2,4,15}*1440, {3,2,4,30}*1440b, {3,2,4,30}*1440c, {6,2,4,15}*1440, {15,2,4,3}*1440, {15,2,4,6}*1440b, {15,2,4,6}*1440c, {30,2,4,3}*1440
   11-fold covers : {3,2,4,33}*1584, {33,2,4,3}*1584
   12-fold covers : {9,2,4,12}*1728b, {9,2,4,12}*1728c, {36,2,4,3}*1728, {9,2,8,3}*1728, {3,2,4,36}*1728b, {3,2,4,36}*1728c, {12,2,4,9}*1728, {3,2,8,9}*1728, {9,2,4,6}*1728, {18,2,4,3}*1728, {18,2,4,6}*1728b, {18,2,4,6}*1728c, {3,2,4,18}*1728, {6,2,4,9}*1728, {6,2,4,18}*1728b, {6,2,4,18}*1728c, {3,2,24,3}*1728, {3,6,8,3}*1728, {3,6,4,6}*1728b, {6,6,4,3}*1728a, {6,6,4,3}*1728c, {3,2,12,6}*1728a, {3,2,12,6}*1728b, {6,2,12,3}*1728, {6,2,12,6}*1728d
   13-fold covers : {3,2,4,39}*1872, {39,2,4,3}*1872
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5)(6,7);;
s3 := (5,6);;
s4 := (6,7);;
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, 
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s2*s3*s4*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(7)!(2,3);
s1 := Sym(7)!(1,2);
s2 := Sym(7)!(4,5)(6,7);
s3 := Sym(7)!(5,6);
s4 := Sym(7)!(6,7);
poly := sub<Sym(7)|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, s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s2*s3*s4*s2*s3 >;

to this polytope