Polytope of Type {3,4,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,4,2,4}*192
if this polytope has a name.
Group : SmallGroup(192,1472)
Rank : 5
Schlafli Type : {3,4,2,4}
Number of vertices, edges, etc : 3, 6, 4, 4, 4
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,4,2,4,2} of size 384
   {3,4,2,4,3} of size 576
   {3,4,2,4,4} of size 768
   {3,4,2,4,6} of size 1152
   {3,4,2,4,3} of size 1152
   {3,4,2,4,6} of size 1152
   {3,4,2,4,6} of size 1152
   {3,4,2,4,9} of size 1728
   {3,4,2,4,4} of size 1728
   {3,4,2,4,6} of size 1728
   {3,4,2,4,10} of size 1920
Vertex Figure Of :
   {2,3,4,2,4} of size 384
   {4,3,4,2,4} of size 768
   {6,3,4,2,4} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,4,2,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,4,2,8}*384, {3,4,2,4}*384, {6,4,2,4}*384b, {6,4,2,4}*384c
   3-fold covers : {9,4,2,4}*576, {3,4,2,12}*576
   4-fold covers : {3,4,4,4}*768a, {3,4,2,16}*768, {3,4,4,4}*768b, {12,4,2,4}*768b, {12,4,2,4}*768c, {3,4,2,8}*768, {6,4,2,8}*768b, {6,4,2,8}*768c, {3,8,2,4}*768, {6,4,2,4}*768
   5-fold covers : {3,4,2,20}*960, {15,4,2,4}*960
   6-fold covers : {9,4,2,8}*1152, {9,4,2,4}*1152, {18,4,2,4}*1152b, {18,4,2,4}*1152c, {3,4,2,24}*1152, {3,4,2,12}*1152, {6,4,2,12}*1152b, {6,4,2,12}*1152c, {3,4,6,4}*1152a, {3,12,2,4}*1152, {6,12,2,4}*1152d
   7-fold covers : {3,4,2,28}*1344, {21,4,2,4}*1344
   9-fold covers : {27,4,2,4}*1728, {3,4,2,36}*1728, {9,4,2,12}*1728
   10-fold covers : {3,4,2,40}*1920, {15,4,2,8}*1920, {3,4,2,20}*1920, {6,4,2,20}*1920b, {6,4,2,20}*1920c, {3,4,10,4}*1920, {6,20,2,4}*1920b, {15,4,2,4}*1920, {30,4,2,4}*1920b, {30,4,2,4}*1920c
Permutation Representation (GAP) :

s0 := (3,4);;
s1 := (2,3);;
s2 := (1,2)(3,4);;
s3 := (6,7);;
s4 := (5,6)(7,8);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4, s0*s2*s1*s0*s2*s1*s0*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(8)!(3,4);
s1 := Sym(8)!(2,3);
s2 := Sym(8)!(1,2)(3,4);
s3 := Sym(8)!(6,7);
s4 := Sym(8)!(5,6)(7,8);
poly := sub<Sym(8)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s2*s1*s0*s2*s1*s0*s2*s1 >;

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