Polytope of Type {6,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,2}*144c
if this polytope has a name.
Group : SmallGroup(144,192)
Rank : 4
Schlafli Type : {6,6,2}
Number of vertices, edges, etc : 6, 18, 6, 2
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,6,2,2} of size 288
   {6,6,2,3} of size 432
   {6,6,2,4} of size 576
   {6,6,2,5} of size 720
   {6,6,2,6} of size 864
   {6,6,2,7} of size 1008
   {6,6,2,8} of size 1152
   {6,6,2,9} of size 1296
   {6,6,2,10} of size 1440
   {6,6,2,11} of size 1584
   {6,6,2,12} of size 1728
   {6,6,2,13} of size 1872
Vertex Figure Of :
   {2,6,6,2} of size 288
   {4,6,6,2} of size 576
   {4,6,6,2} of size 576
   {4,6,6,2} of size 576
   {6,6,6,2} of size 864
   {6,6,6,2} of size 864
   {8,6,6,2} of size 1152
   {4,6,6,2} of size 1152
   {6,6,6,2} of size 1296
   {10,6,6,2} of size 1440
   {12,6,6,2} of size 1728
   {12,6,6,2} of size 1728
   {12,6,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,6,2}*72
   3-fold quotients : {6,2,2}*48
   6-fold quotients : {3,2,2}*24
   9-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,6,2}*288b, {6,6,4}*288c, {6,12,2}*288c
   3-fold covers : {18,6,2}*432b, {6,6,2}*432c, {6,6,6}*432g, {6,6,2}*432d
   4-fold covers : {24,6,2}*576b, {12,12,2}*576c, {12,6,4}*576b, {6,6,8}*576c, {6,24,2}*576c, {6,12,4}*576c, {6,6,2}*576b, {6,12,2}*576b
   5-fold covers : {6,6,10}*720c, {6,30,2}*720a, {30,6,2}*720c
   6-fold covers : {36,6,2}*864b, {12,6,2}*864a, {18,6,4}*864b, {18,12,2}*864b, {6,6,4}*864c, {6,12,2}*864c, {12,6,6}*864d, {6,6,12}*864e, {6,12,2}*864g, {12,6,2}*864g, {6,6,4}*864h, {6,12,6}*864f
   7-fold covers : {6,6,14}*1008c, {6,42,2}*1008a, {42,6,2}*1008c
   8-fold covers : {12,12,4}*1152c, {6,12,8}*1152c, {6,24,4}*1152a, {24,12,2}*1152b, {12,24,2}*1152c, {6,12,8}*1152f, {6,24,4}*1152d, {24,12,2}*1152e, {12,24,2}*1152f, {6,12,4}*1152c, {12,12,2}*1152c, {12,6,8}*1152c, {24,6,4}*1152c, {6,6,16}*1152c, {6,48,2}*1152a, {48,6,2}*1152c, {12,12,2}*1152e, {12,6,2}*1152a, {12,12,2}*1152h, {6,12,2}*1152c, {6,24,2}*1152b, {6,6,2}*1152b, {6,24,2}*1152d, {12,6,2}*1152d, {6,6,4}*1152f, {6,12,4}*1152j, {6,12,2}*1152e, {6,12,2}*1152f
   9-fold covers : {18,18,2}*1296c, {18,6,2}*1296a, {54,6,2}*1296b, {18,6,2}*1296c, {18,6,2}*1296d, {18,6,2}*1296e, {6,6,2}*1296d, {6,18,2}*1296h, {6,6,18}*1296e, {18,6,6}*1296e, {6,18,2}*1296i, {18,6,2}*1296i, {6,6,6}*1296c, {6,6,6}*1296o, {6,6,6}*1296p, {6,6,2}*1296e, {6,6,2}*1296f, {6,6,2}*1296g, {6,6,6}*1296s, {6,6,6}*1296t
   10-fold covers : {12,6,10}*1440b, {6,6,20}*1440c, {6,60,2}*1440a, {12,30,2}*1440a, {6,12,10}*1440c, {6,30,4}*1440a, {60,6,2}*1440c, {30,6,4}*1440c, {30,12,2}*1440c
   11-fold covers : {6,6,22}*1584c, {6,66,2}*1584a, {66,6,2}*1584c
   12-fold covers : {72,6,2}*1728b, {24,6,2}*1728a, {36,12,2}*1728b, {36,6,4}*1728b, {12,12,2}*1728a, {12,6,4}*1728b, {18,6,8}*1728b, {18,24,2}*1728b, {6,6,8}*1728c, {6,24,2}*1728c, {18,12,4}*1728b, {6,12,4}*1728c, {24,6,6}*1728d, {6,6,24}*1728e, {6,24,2}*1728f, {24,6,2}*1728f, {12,6,12}*1728f, {12,12,6}*1728f, {6,6,8}*1728e, {6,24,6}*1728g, {12,12,2}*1728h, {6,12,4}*1728j, {6,12,12}*1728g, {12,6,4}*1728h, {18,6,2}*1728, {18,12,2}*1728b, {6,6,2}*1728a, {6,12,2}*1728a, {6,6,4}*1728c, {6,6,6}*1728f, {6,12,6}*1728h, {6,12,6}*1728l, {6,6,2}*1728c, {6,12,2}*1728c, {12,6,2}*1728c
   13-fold covers : {6,6,26}*1872c, {6,78,2}*1872a, {78,6,2}*1872c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope