Polytope of Type {12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6}*192a
if this polytope has a name.
Group : SmallGroup(192,1472)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 16, 48, 8
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {12,6,2} of size 384
   {12,6,4} of size 768
   {12,6,3} of size 960
   {12,6,6} of size 1152
   {12,6,10} of size 1920
   {12,6,6} of size 1920
Vertex Figure Of :
   {2,12,6} of size 384
   {4,12,6} of size 768
   {6,12,6} of size 1152
   {6,12,6} of size 1152
   {6,12,6} of size 1728
   {10,12,6} of size 1920
   {6,12,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6}*96
   4-fold quotients : {3,6}*48, {6,3}*48
   8-fold quotients : {3,3}*24
   12-fold quotients : {4,2}*16
   24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,12}*384a, {12,6}*384, {12,12}*384d, {24,6}*384a, {24,6}*384b
   3-fold covers : {12,6}*576a, {12,6}*576e
   4-fold covers : {24,6}*768, {24,12}*768a, {24,12}*768b, {12,6}*768f, {12,12}*768a, {12,12}*768b, {12,12}*768c, {12,24}*768c, {24,12}*768c, {12,24}*768d, {24,12}*768d, {12,6}*768g, {12,24}*768e, {24,12}*768e, {12,24}*768f, {24,12}*768f, {12,6}*768h, {48,6}*768a, {48,6}*768b
   5-fold covers : {60,6}*960a, {12,30}*960b
   6-fold covers : {12,12}*1152g, {12,6}*1152a, {24,6}*1152g, {24,6}*1152i, {12,12}*1152j, {12,12}*1152l, {24,6}*1152j, {12,6}*1152e, {12,12}*1152p, {24,6}*1152m
   7-fold covers : {84,6}*1344a, {12,42}*1344b
   9-fold covers : {36,6}*1728a, {12,18}*1728b, {12,6}*1728a, {12,6}*1728e, {12,6}*1728h, {12,6}*1728j
   10-fold covers : {60,12}*1920b, {60,6}*1920, {120,6}*1920a, {120,6}*1920b, {12,60}*1920c, {60,12}*1920c, {24,30}*1920a, {12,30}*1920, {12,60}*1920d, {24,30}*1920b
Permutation Representation (GAP) :

s0 := ( 1, 5)( 2, 6)( 7,12)( 8,11)( 9,10);;
s1 := ( 1, 7)( 2, 8)( 3,11)( 4,12)( 5, 9)( 6,10);;
s2 := ( 1, 5)( 2, 6)( 3, 4)( 7,11)( 8,12)( 9,10);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope