Polytope of Type {4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,12}*192c
if this polytope has a name.
Group : SmallGroup(192,1472)
Rank : 3
Schlafli Type : {4,12}
Number of vertices, edges, etc : 8, 48, 24
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {4,12,2} of size 384
   {4,12,3} of size 768
   {4,12,3} of size 768
   {4,12,4} of size 768
   {4,12,4} of size 768
   {4,12,4} of size 768
   {4,12,6} of size 1152
   {4,12,6} of size 1152
   {4,12,10} of size 1920
Vertex Figure Of :
   {2,4,12} of size 384
   {4,4,12} of size 768
   {6,4,12} of size 1152
   {10,4,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6}*96
   4-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   8-fold quotients : {4,3}*24, {2,6}*24
   16-fold quotients : {2,3}*12
   24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12}*384d, {8,12}*384g, {8,12}*384h, {4,24}*384e, {4,24}*384f
   3-fold covers : {4,36}*576c, {12,12}*576i, {12,12}*576k
   4-fold covers : {8,24}*768m, {8,24}*768n, {8,24}*768o, {8,24}*768p, {4,12}*768c, {8,12}*768s, {4,24}*768i, {4,12}*768d, {8,12}*768t, {4,24}*768j, {8,12}*768u, {4,12}*768e, {4,24}*768k, {8,12}*768v, {8,12}*768w, {4,12}*768f, {4,24}*768l, {8,12}*768x
   5-fold covers : {20,12}*960c, {4,60}*960c
   6-fold covers : {4,36}*1152d, {8,36}*1152g, {8,36}*1152h, {4,72}*1152e, {4,72}*1152f, {24,12}*1152m, {24,12}*1152n, {12,24}*1152s, {12,24}*1152t, {12,12}*1152n, {12,12}*1152o, {24,12}*1152u, {24,12}*1152v, {12,24}*1152w, {12,24}*1152x
   7-fold covers : {28,12}*1344c, {4,84}*1344c
   9-fold covers : {4,108}*1728c, {36,12}*1728d, {12,36}*1728g, {12,12}*1728n, {12,36}*1728h, {12,12}*1728p, {12,12}*1728y, {4,12}*1728e
   10-fold covers : {20,12}*1920c, {40,12}*1920g, {40,12}*1920h, {20,24}*1920e, {20,24}*1920f, {4,60}*1920d, {8,60}*1920g, {8,60}*1920h, {4,120}*1920e, {4,120}*1920f
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope