Polytope of Type {4,4,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,3}*192a
Also Known As : {{4,4}4,{4,3}3}. if this polytope has another name.
Group : SmallGroup(192,955)
Rank : 4
Schlafli Type : {4,4,3}
Number of vertices, edges, etc : 8, 16, 12, 3
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 4
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,4,3,2} of size 384
{4,4,3,4} of size 768
{4,4,3,6} of size 1152
Vertex Figure Of :
{2,4,4,3} of size 384
{3,4,4,3} of size 576
{4,4,4,3} of size 768
{6,4,4,3} of size 1152
{6,4,4,3} of size 1152
{9,4,4,3} of size 1728
{10,4,4,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
4-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,4,3}*384a, {4,4,3}*384b, {4,4,6}*384b, {4,4,6}*384c
3-fold covers : {4,4,9}*576a
4-fold covers : {8,4,3}*768a, {8,4,3}*768b, {4,8,3}*768a, {4,8,3}*768b, {4,4,3}*768a, {4,4,6}*768b, {4,4,12}*768c, {4,4,12}*768d, {4,4,3}*768b, {4,4,6}*768c, {4,4,6}*768d, {4,4,3}*768c, {4,8,3}*768e, {4,8,3}*768f, {4,4,6}*768f
5-fold covers : {4,4,15}*960a
6-fold covers : {4,4,9}*1152a, {4,4,9}*1152b, {4,4,18}*1152b, {4,4,18}*1152c, {4,12,3}*1152a, {4,12,6}*1152d, {12,4,3}*1152
7-fold covers : {4,4,21}*1344a
9-fold covers : {4,4,27}*1728a
10-fold covers : {4,4,15}*1920a, {4,20,6}*1920b, {20,4,3}*1920, {4,4,15}*1920b, {4,4,30}*1920b, {4,4,30}*1920c
Permutation Representation (GAP) :
s0 := ( 3, 4)( 7, 8)(11,12);;
s1 := ( 5, 7)( 6, 8)( 9,11)(10,12);;
s2 := (1,5)(2,6)(3,7)(4,8);;
s3 := ( 5, 9)( 6,10)( 7,11)( 8,12);;
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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s1*s2*s3*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(12)!( 3, 4)( 7, 8)(11,12);
s1 := Sym(12)!( 5, 7)( 6, 8)( 9,11)(10,12);
s2 := Sym(12)!(1,5)(2,6)(3,7)(4,8);
s3 := Sym(12)!( 5, 9)( 6,10)( 7,11)( 8,12);
poly := sub<Sym(12)|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, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;
References : None.
to this polytope