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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,4,2,2}*96
if this polytope has a name.
Group : SmallGroup(96,226)
Rank : 5
Schlafli Type : {3,4,2,2}
Number of vertices, edges, etc : 3, 6, 4, 2, 2
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,4,2,2,2} of size 192
   {3,4,2,2,3} of size 288
   {3,4,2,2,4} of size 384
   {3,4,2,2,5} of size 480
   {3,4,2,2,6} of size 576
   {3,4,2,2,7} of size 672
   {3,4,2,2,8} of size 768
   {3,4,2,2,9} of size 864
   {3,4,2,2,10} of size 960
   {3,4,2,2,11} of size 1056
   {3,4,2,2,12} of size 1152
   {3,4,2,2,13} of size 1248
   {3,4,2,2,14} of size 1344
   {3,4,2,2,15} of size 1440
   {3,4,2,2,17} of size 1632
   {3,4,2,2,18} of size 1728
   {3,4,2,2,19} of size 1824
   {3,4,2,2,20} of size 1920
Vertex Figure Of :
   {2,3,4,2,2} of size 192
   {4,3,4,2,2} of size 384
   {6,3,4,2,2} of size 576
   {4,3,4,2,2} of size 768
   {6,3,4,2,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,4,2,4}*192, {3,4,2,2}*192, {6,4,2,2}*192b, {6,4,2,2}*192c
   3-fold covers : {9,4,2,2}*288, {3,4,2,6}*288
   4-fold covers : {3,4,4,2}*384a, {3,4,2,8}*384, {12,4,2,2}*384b, {12,4,2,2}*384c, {3,4,2,4}*384, {3,4,4,2}*384b, {6,4,2,4}*384b, {6,4,2,4}*384c, {3,8,2,2}*384, {6,4,2,2}*384
   5-fold covers : {3,4,2,10}*480, {15,4,2,2}*480
   6-fold covers : {9,4,2,4}*576, {9,4,2,2}*576, {18,4,2,2}*576b, {18,4,2,2}*576c, {3,4,2,12}*576, {3,4,2,6}*576, {3,4,6,2}*576, {3,12,2,2}*576, {6,4,2,6}*576b, {6,4,2,6}*576c, {6,12,2,2}*576d
   7-fold covers : {3,4,2,14}*672, {21,4,2,2}*672
   8-fold covers : {3,4,4,4}*768a, {3,4,4,2}*768a, {3,4,2,16}*768, {3,4,4,4}*768b, {12,4,2,4}*768b, {12,4,2,4}*768c, {3,8,2,2}*768, {6,8,2,2}*768a, {3,4,4,2}*768b, {6,4,2,2}*768a, {6,4,4,2}*768b, {6,4,4,2}*768c, {24,4,2,2}*768c, {24,4,2,2}*768d, {3,8,4,2}*768, {3,4,2,8}*768, {3,4,8,2}*768, {6,4,2,8}*768b, {6,4,2,8}*768c, {3,8,2,4}*768, {12,4,2,2}*768b, {6,4,2,2}*768b, {6,4,2,4}*768, {6,4,4,2}*768d, {12,4,2,2}*768c, {6,8,2,2}*768b, {6,8,2,2}*768c
   9-fold covers : {27,4,2,2}*864, {3,4,2,18}*864, {9,4,2,6}*864
   10-fold covers : {3,4,2,20}*960, {15,4,2,4}*960, {3,4,2,10}*960, {3,4,10,2}*960, {6,4,2,10}*960b, {6,4,2,10}*960c, {6,20,2,2}*960b, {15,4,2,2}*960, {30,4,2,2}*960b, {30,4,2,2}*960c
   11-fold covers : {3,4,2,22}*1056, {33,4,2,2}*1056
   12-fold covers : {9,4,4,2}*1152a, {9,4,2,8}*1152, {36,4,2,2}*1152b, {36,4,2,2}*1152c, {9,4,2,4}*1152, {9,4,4,2}*1152b, {18,4,2,4}*1152b, {18,4,2,4}*1152c, {9,8,2,2}*1152, {3,4,4,6}*1152a, {3,4,2,24}*1152, {18,4,2,2}*1152, {12,4,2,6}*1152b, {12,4,2,6}*1152c, {3,4,2,12}*1152, {3,4,12,2}*1152, {6,4,2,12}*1152b, {6,4,2,12}*1152c, {3,4,4,6}*1152b, {3,4,6,4}*1152a, {3,12,2,4}*1152, {6,12,2,4}*1152d, {3,24,2,2}*1152, {3,8,2,6}*1152, {3,8,6,2}*1152, {3,12,4,2}*1152, {6,4,2,6}*1152, {6,4,6,2}*1152b, {6,12,2,2}*1152a, {6,12,2,2}*1152b
   13-fold covers : {3,4,2,26}*1248, {39,4,2,2}*1248
   14-fold covers : {3,4,2,28}*1344, {21,4,2,4}*1344, {3,4,2,14}*1344, {3,4,14,2}*1344, {6,4,2,14}*1344b, {6,4,2,14}*1344c, {6,28,2,2}*1344b, {21,4,2,2}*1344, {42,4,2,2}*1344b, {42,4,2,2}*1344c
   15-fold covers : {9,4,2,10}*1440, {45,4,2,2}*1440, {15,4,2,6}*1440, {3,4,2,30}*1440
   17-fold covers : {3,4,2,34}*1632, {51,4,2,2}*1632
   18-fold covers : {27,4,2,4}*1728, {27,4,2,2}*1728, {54,4,2,2}*1728b, {54,4,2,2}*1728c, {3,4,2,36}*1728, {9,4,2,12}*1728, {3,4,2,18}*1728, {3,4,18,2}*1728, {6,4,2,18}*1728b, {6,4,2,18}*1728c, {6,36,2,2}*1728c, {9,4,2,6}*1728, {9,4,6,2}*1728, {9,12,2,2}*1728, {18,4,2,6}*1728b, {18,4,2,6}*1728c, {18,12,2,2}*1728c, {3,12,2,2}*1728, {3,12,6,2}*1728a, {6,12,2,2}*1728d, {3,4,6,6}*1728a, {3,4,6,6}*1728b, {3,4,6,6}*1728c, {3,12,2,6}*1728, {3,12,6,2}*1728b, {6,12,2,6}*1728d, {6,12,6,2}*1728i
   19-fold covers : {3,4,2,38}*1824, {57,4,2,2}*1824
   20-fold covers : {3,4,4,10}*1920a, {3,4,2,40}*1920, {15,4,4,2}*1920a, {15,4,2,8}*1920, {12,4,2,10}*1920b, {12,4,2,10}*1920c, {3,4,2,20}*1920, {3,4,20,2}*1920, {6,4,2,20}*1920b, {6,4,2,20}*1920c, {3,4,4,10}*1920b, {3,4,10,4}*1920, {6,20,2,4}*1920b, {3,8,2,10}*1920, {3,8,10,2}*1920, {60,4,2,2}*1920b, {60,4,2,2}*1920c, {15,4,2,4}*1920, {15,4,4,2}*1920b, {30,4,2,4}*1920b, {30,4,2,4}*1920c, {15,8,2,2}*1920, {6,4,2,10}*1920, {6,4,10,2}*1920, {6,20,2,2}*1920a, {30,4,2,2}*1920
Permutation Representation (GAP) :

s0 := (3,4);;
s1 := (2,3);;
s2 := (1,2)(3,4);;
s3 := (5,6);;
s4 := (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, 
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
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)!(5,6);
s4 := Sym(8)!(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, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s0*s2*s1*s0*s2*s1 >;

to this polytope