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

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

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

Permutation Representation (Magma) :

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

to this polytope