Polytope of Type {12,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,3}*144
if this polytope has a name.
Group : SmallGroup(144,144)
Rank : 4
Schlafli Type : {12,2,3}
Number of vertices, edges, etc : 12, 12, 3, 3
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,2,3,2} of size 288
   {12,2,3,3} of size 576
   {12,2,3,4} of size 576
   {12,2,3,6} of size 864
   {12,2,3,4} of size 1152
   {12,2,3,6} of size 1152
   {12,2,3,5} of size 1440
Vertex Figure Of :
   {2,12,2,3} of size 288
   {4,12,2,3} of size 576
   {4,12,2,3} of size 576
   {4,12,2,3} of size 576
   {3,12,2,3} of size 576
   {6,12,2,3} of size 864
   {6,12,2,3} of size 864
   {6,12,2,3} of size 864
   {3,12,2,3} of size 864
   {6,12,2,3} of size 864
   {8,12,2,3} of size 1152
   {8,12,2,3} of size 1152
   {4,12,2,3} of size 1152
   {4,12,2,3} of size 1152
   {4,12,2,3} of size 1152
   {6,12,2,3} of size 1152
   {6,12,2,3} of size 1152
   {4,12,2,3} of size 1296
   {6,12,2,3} of size 1296
   {6,12,2,3} of size 1296
   {6,12,2,3} of size 1296
   {10,12,2,3} of size 1440
   {12,12,2,3} of size 1728
   {12,12,2,3} of size 1728
   {12,12,2,3} of size 1728
   {3,12,2,3} of size 1728
   {4,12,2,3} of size 1728
   {6,12,2,3} of size 1728
   {6,12,2,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,2,3}*72
   3-fold quotients : {4,2,3}*48
   4-fold quotients : {3,2,3}*36
   6-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,2,3}*288, {12,2,6}*288
   3-fold covers : {36,2,3}*432, {12,2,9}*432, {12,6,3}*432a, {12,6,3}*432b
   4-fold covers : {48,2,3}*576, {12,2,12}*576, {12,4,6}*576, {24,2,6}*576, {12,4,3}*576
   5-fold covers : {12,2,15}*720, {60,2,3}*720
   6-fold covers : {72,2,3}*864, {24,2,9}*864, {24,6,3}*864a, {36,2,6}*864, {12,2,18}*864, {12,6,6}*864a, {24,6,3}*864b, {12,6,6}*864b, {12,6,6}*864d, {12,6,6}*864e
   7-fold covers : {12,2,21}*1008, {84,2,3}*1008
   8-fold covers : {96,2,3}*1152, {12,4,12}*1152, {12,8,6}*1152a, {24,4,6}*1152a, {12,8,6}*1152b, {24,4,6}*1152b, {12,4,6}*1152a, {12,2,24}*1152, {24,2,12}*1152, {48,2,6}*1152, {12,8,3}*1152, {24,4,3}*1152, {12,4,6}*1152b, {12,4,6}*1152c
   9-fold covers : {36,2,9}*1296, {12,6,9}*1296a, {36,6,3}*1296a, {12,2,27}*1296, {108,2,3}*1296, {12,6,3}*1296a, {12,6,3}*1296b, {36,6,3}*1296b, {12,6,9}*1296b, {12,6,3}*1296c, {12,6,3}*1296d, {12,6,3}*1296e, {12,6,3}*1296f
   10-fold covers : {24,2,15}*1440, {120,2,3}*1440, {12,10,6}*1440, {12,2,30}*1440, {60,2,6}*1440
   11-fold covers : {12,2,33}*1584, {132,2,3}*1584
   12-fold covers : {144,2,3}*1728, {48,2,9}*1728, {48,6,3}*1728a, {12,2,36}*1728, {36,2,12}*1728, {12,6,12}*1728a, {12,4,18}*1728, {36,4,6}*1728, {12,12,6}*1728a, {72,2,6}*1728, {24,2,18}*1728, {24,6,6}*1728a, {48,6,3}*1728b, {36,4,3}*1728, {12,4,9}*1728, {12,12,3}*1728a, {24,6,6}*1728b, {24,6,6}*1728d, {24,6,6}*1728e, {12,6,12}*1728b, {12,6,12}*1728e, {12,6,12}*1728f, {12,12,6}*1728b, {12,12,6}*1728f, {12,12,6}*1728g, {12,6,3}*1728, {12,12,3}*1728b
   13-fold covers : {12,2,39}*1872, {156,2,3}*1872
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope