Polytope of Type {3,2,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,6,2}*144
if this polytope has a name.
Group : SmallGroup(144,192)
Rank : 5
Schlafli Type : {3,2,6,2}
Number of vertices, edges, etc : 3, 3, 6, 6, 2
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,6,2,2} of size 288
   {3,2,6,2,3} of size 432
   {3,2,6,2,4} of size 576
   {3,2,6,2,5} of size 720
   {3,2,6,2,6} of size 864
   {3,2,6,2,7} of size 1008
   {3,2,6,2,8} of size 1152
   {3,2,6,2,9} of size 1296
   {3,2,6,2,10} of size 1440
   {3,2,6,2,11} of size 1584
   {3,2,6,2,12} of size 1728
   {3,2,6,2,13} of size 1872
Vertex Figure Of :
   {2,3,2,6,2} of size 288
   {3,3,2,6,2} of size 576
   {4,3,2,6,2} of size 576
   {6,3,2,6,2} of size 864
   {4,3,2,6,2} of size 1152
   {6,3,2,6,2} of size 1152
   {5,3,2,6,2} of size 1440
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,3,2}*72
   3-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,12,2}*288, {3,2,6,4}*288a, {6,2,6,2}*288
   3-fold covers : {3,2,18,2}*432, {9,2,6,2}*432, {3,6,6,2}*432a, {3,2,6,6}*432a, {3,2,6,6}*432c, {3,6,6,2}*432b
   4-fold covers : {3,2,12,4}*576a, {3,2,24,2}*576, {3,2,6,8}*576, {6,2,12,2}*576, {12,2,6,2}*576, {6,2,6,4}*576a, {6,4,6,2}*576, {3,2,6,4}*576, {3,4,6,2}*576
   5-fold covers : {3,2,6,10}*720, {3,2,30,2}*720, {15,2,6,2}*720
   6-fold covers : {3,2,36,2}*864, {9,2,12,2}*864, {3,6,12,2}*864a, {3,2,18,4}*864a, {9,2,6,4}*864a, {3,6,6,4}*864a, {6,2,18,2}*864, {18,2,6,2}*864, {6,6,6,2}*864a, {3,2,6,12}*864a, {3,2,12,6}*864a, {3,2,12,6}*864b, {3,6,12,2}*864b, {3,2,6,12}*864c, {3,6,6,4}*864d, {6,2,6,6}*864a, {6,2,6,6}*864c, {6,6,6,2}*864b, {6,6,6,2}*864c, {6,6,6,2}*864g
   7-fold covers : {3,2,6,14}*1008, {3,2,42,2}*1008, {21,2,6,2}*1008
   8-fold covers : {3,2,12,8}*1152a, {3,2,24,4}*1152a, {3,2,12,8}*1152b, {3,2,24,4}*1152b, {3,2,12,4}*1152a, {3,2,6,16}*1152, {3,2,48,2}*1152, {6,2,12,4}*1152a, {6,4,12,2}*1152, {12,4,6,2}*1152, {6,4,6,4}*1152a, {12,2,6,4}*1152a, {12,2,12,2}*1152, {6,2,6,8}*1152, {6,8,6,2}*1152, {6,2,24,2}*1152, {24,2,6,2}*1152, {3,2,12,4}*1152b, {3,4,12,2}*1152, {3,4,6,4}*1152a, {3,2,6,4}*1152b, {3,2,12,4}*1152c, {3,2,6,8}*1152b, {3,8,6,2}*1152, {3,2,6,8}*1152c, {6,2,6,4}*1152, {6,4,6,2}*1152a, {6,4,6,2}*1152b
   9-fold covers : {9,2,18,2}*1296, {3,6,18,2}*1296a, {9,6,6,2}*1296a, {3,2,54,2}*1296, {27,2,6,2}*1296, {3,6,6,2}*1296a, {3,6,6,2}*1296b, {3,2,6,18}*1296a, {3,2,18,6}*1296a, {3,2,18,6}*1296b, {3,6,18,2}*1296b, {9,2,6,6}*1296a, {9,2,6,6}*1296c, {9,6,6,2}*1296b, {3,6,6,6}*1296a, {3,6,6,6}*1296b, {3,2,6,6}*1296b, {3,2,6,6}*1296c, {3,6,6,2}*1296c, {3,6,6,2}*1296d, {3,6,6,2}*1296e, {3,6,6,6}*1296c, {3,6,6,6}*1296d, {3,2,6,6}*1296d
   10-fold covers : {3,2,12,10}*1440, {3,2,6,20}*1440a, {15,2,12,2}*1440, {3,2,60,2}*1440, {3,2,30,4}*1440a, {15,2,6,4}*1440a, {6,2,6,10}*1440, {6,10,6,2}*1440, {6,2,30,2}*1440, {30,2,6,2}*1440
   11-fold covers : {3,2,6,22}*1584, {3,2,66,2}*1584, {33,2,6,2}*1584
   12-fold covers : {9,2,12,4}*1728a, {3,2,36,4}*1728a, {3,6,12,4}*1728a, {3,2,72,2}*1728, {9,2,24,2}*1728, {3,6,24,2}*1728a, {3,2,18,8}*1728, {9,2,6,8}*1728, {3,6,6,8}*1728a, {12,2,18,2}*1728, {18,2,12,2}*1728, {6,2,36,2}*1728, {36,2,6,2}*1728, {6,6,12,2}*1728a, {12,6,6,2}*1728a, {6,2,18,4}*1728a, {6,4,18,2}*1728, {18,2,6,4}*1728a, {18,4,6,2}*1728, {6,6,6,4}*1728a, {6,12,6,2}*1728a, {3,2,6,24}*1728a, {3,2,24,6}*1728a, {3,2,24,6}*1728b, {3,6,24,2}*1728b, {3,2,12,12}*1728a, {3,2,12,12}*1728c, {3,2,6,24}*1728c, {3,6,6,8}*1728b, {3,6,12,4}*1728d, {3,4,18,2}*1728, {9,2,6,4}*1728, {3,2,18,4}*1728, {9,4,6,2}*1728, {3,6,6,4}*1728a, {3,12,6,2}*1728a, {6,2,6,12}*1728a, {6,2,12,6}*1728a, {6,2,12,6}*1728b, {6,6,12,2}*1728b, {6,6,12,2}*1728c, {6,12,6,2}*1728b, {12,2,6,6}*1728a, {12,2,6,6}*1728c, {12,6,6,2}*1728b, {12,6,6,2}*1728d, {6,4,6,6}*1728a, {6,4,6,6}*1728b, {6,6,6,4}*1728d, {6,6,6,4}*1728e, {6,6,12,2}*1728e, {12,6,6,2}*1728e, {6,2,6,12}*1728c, {6,12,6,2}*1728f, {6,12,6,2}*1728g, {6,6,6,4}*1728i, {3,4,6,6}*1728a, {3,4,6,6}*1728c, {3,6,6,4}*1728b, {3,2,6,6}*1728b, {3,2,6,12}*1728a, {3,2,6,12}*1728b, {3,2,12,6}*1728a, {3,6,6,2}*1728, {3,12,6,2}*1728b
   13-fold covers : {3,2,6,26}*1872, {3,2,78,2}*1872, {39,2,6,2}*1872
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope