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Polytope of Type {6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4}*192b
if this polytope has a name.
Group : SmallGroup(192,1472)
Rank : 3
Schlafli Type : {6,4}
Number of vertices, edges, etc : 24, 48, 16
Order of s0s1s2 : 12
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {6,4,2} of size 384
   {6,4,4} of size 768
   {6,4,6} of size 1152
   {6,4,10} of size 1920
Vertex Figure Of :
   {2,6,4} of size 384
   {3,6,4} of size 768
   {3,6,4} of size 768
   {4,6,4} of size 768
   {4,6,4} of size 768
   {4,6,4} of size 768
   {6,6,4} of size 1152
   {6,6,4} of size 1152
   {4,6,4} of size 1152
   {10,6,4} of size 1920
   {6,6,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4}*96
   4-fold quotients : {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   8-fold quotients : {3,4}*24, {6,2}*24
   12-fold quotients : {2,4}*16
   16-fold quotients : {3,2}*12
   24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,4}*384d, {6,8}*384f, {6,8}*384g, {12,4}*384e, {6,4}*384b
   3-fold covers : {18,4}*576b, {6,12}*576b, {6,12}*576f
   4-fold covers : {6,8}*768j, {12,8}*768o, {12,8}*768p, {6,4}*768a, {12,8}*768s, {24,4}*768i, {12,4}*768d, {12,8}*768t, {24,4}*768j, {12,8}*768u, {12,4}*768e, {24,4}*768k, {6,8}*768k, {12,8}*768w, {12,4}*768f, {24,4}*768l, {6,8}*768l, {6,16}*768b, {6,16}*768c
   5-fold covers : {6,20}*960e, {30,4}*960b
   6-fold covers : {36,4}*1152d, {18,8}*1152f, {18,8}*1152g, {36,4}*1152e, {18,4}*1152b, {6,24}*1152d, {6,24}*1152h, {6,12}*1152d, {12,12}*1152h, {12,12}*1152k, {12,12}*1152m, {6,24}*1152k, {6,24}*1152l, {12,12}*1152s, {6,12}*1152f
   7-fold covers : {6,28}*1344e, {42,4}*1344b
   9-fold covers : {54,4}*1728b, {6,36}*1728b, {18,12}*1728c, {6,12}*1728b, {18,12}*1728d, {6,12}*1728f, {6,12}*1728i, {6,4}*1728
   10-fold covers : {6,40}*1920b, {6,40}*1920d, {6,20}*1920b, {12,20}*1920b, {12,20}*1920c, {60,4}*1920d, {30,8}*1920f, {30,8}*1920g, {60,4}*1920e, {30,4}*1920b
Permutation Representation (GAP) :
s0 := ( 1, 5)( 2, 6)( 7,11)( 8,12);;
s1 := ( 3, 5)( 4, 6)( 7, 8)( 9,12)(10,11);;
s2 := ( 1, 7)( 2, 8)( 3,10)( 4, 9)( 5,11)( 6,12);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(12)!( 1, 5)( 2, 6)( 7,11)( 8,12);
s1 := Sym(12)!( 3, 5)( 4, 6)( 7, 8)( 9,12)(10,11);
s2 := Sym(12)!( 1, 7)( 2, 8)( 3,10)( 4, 9)( 5,11)( 6,12);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1 >; 
 
References : None.
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