Polytope of Type {12,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,4}*192
if this polytope has a name.
Group : SmallGroup(192,1108)
Rank : 4
Schlafli Type : {12,2,4}
Number of vertices, edges, etc : 12, 12, 4, 4
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,2,4,2} of size 384
   {12,2,4,3} of size 576
   {12,2,4,4} of size 768
   {12,2,4,6} of size 1152
   {12,2,4,3} of size 1152
   {12,2,4,6} of size 1152
   {12,2,4,6} of size 1152
   {12,2,4,9} of size 1728
   {12,2,4,4} of size 1728
   {12,2,4,6} of size 1728
   {12,2,4,10} of size 1920
Vertex Figure Of :
   {2,12,2,4} of size 384
   {4,12,2,4} of size 768
   {4,12,2,4} of size 768
   {4,12,2,4} of size 768
   {3,12,2,4} of size 768
   {6,12,2,4} of size 1152
   {6,12,2,4} of size 1152
   {6,12,2,4} of size 1152
   {3,12,2,4} of size 1152
   {6,12,2,4} of size 1152
   {4,12,2,4} of size 1728
   {6,12,2,4} of size 1728
   {6,12,2,4} of size 1728
   {6,12,2,4} of size 1728
   {10,12,2,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,2,2}*96, {6,2,4}*96
   3-fold quotients : {4,2,4}*64
   4-fold quotients : {3,2,4}*48, {6,2,2}*48
   6-fold quotients : {2,2,4}*32, {4,2,2}*32
   8-fold quotients : {3,2,2}*24
   12-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,4,4}*384, {24,2,4}*384, {12,2,8}*384
   3-fold covers : {36,2,4}*576, {12,2,12}*576, {12,6,4}*576a, {12,6,4}*576b
   4-fold covers : {24,2,8}*768, {12,4,8}*768a, {24,4,4}*768a, {12,4,8}*768b, {24,4,4}*768b, {12,8,4}*768a, {12,4,4}*768a, {12,4,4}*768b, {12,8,4}*768b, {12,8,4}*768c, {12,8,4}*768d, {12,2,16}*768, {48,2,4}*768, {12,4,4}*768e
   5-fold covers : {12,2,20}*960, {12,10,4}*960, {60,2,4}*960
   6-fold covers : {36,4,4}*1152, {12,12,4}*1152b, {12,12,4}*1152c, {12,4,12}*1152, {36,2,8}*1152, {72,2,4}*1152, {12,6,8}*1152b, {12,6,8}*1152c, {24,6,4}*1152b, {24,6,4}*1152c, {12,2,24}*1152, {24,2,12}*1152
   7-fold covers : {12,2,28}*1344, {12,14,4}*1344, {84,2,4}*1344
   9-fold covers : {108,2,4}*1728, {12,2,36}*1728, {36,2,12}*1728, {12,6,12}*1728a, {36,6,4}*1728a, {12,18,4}*1728a, {12,6,4}*1728a, {36,6,4}*1728b, {12,6,4}*1728b, {12,6,12}*1728b, {12,6,12}*1728d, {12,6,12}*1728e, {12,6,12}*1728f, {12,6,4}*1728h, {12,6,4}*1728k, {12,6,4}*1728l, {12,6,4}*1728n
   10-fold covers : {60,4,4}*1920, {12,20,4}*1920, {12,4,20}*1920, {60,2,8}*1920, {120,2,4}*1920, {12,10,8}*1920, {24,10,4}*1920, {12,2,40}*1920, {24,2,20}*1920
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)(15,16);;
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*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(16)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(16)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(16)!(14,15);
s3 := Sym(16)!(13,14)(15,16);
poly := sub<Sym(16)|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*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