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Polytope of Type {2,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,4}*96b
if this polytope has a name.
Group : SmallGroup(96,226)
Rank : 4
Schlafli Type : {2,6,4}
Number of vertices, edges, etc : 2, 6, 12, 4
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,4,2} of size 192
   {2,6,4,4} of size 768
Vertex Figure Of :
   {2,2,6,4} of size 192
   {3,2,6,4} of size 288
   {4,2,6,4} of size 384
   {5,2,6,4} of size 480
   {6,2,6,4} of size 576
   {7,2,6,4} of size 672
   {8,2,6,4} of size 768
   {9,2,6,4} of size 864
   {10,2,6,4} of size 960
   {11,2,6,4} of size 1056
   {12,2,6,4} of size 1152
   {13,2,6,4} of size 1248
   {14,2,6,4} of size 1344
   {15,2,6,4} of size 1440
   {17,2,6,4} of size 1632
   {18,2,6,4} of size 1728
   {19,2,6,4} of size 1824
   {20,2,6,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,4}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,4}*192
   3-fold covers : {2,18,4}*288c, {2,6,12}*288d, {6,6,4}*288f
   4-fold covers : {2,6,8}*384a, {2,12,4}*384b, {4,6,4}*384a, {2,6,4}*384b, {2,12,4}*384c, {2,6,8}*384b, {2,6,8}*384c, {4,6,4}*384e
   5-fold covers : {2,6,20}*480b, {2,30,4}*480c
   6-fold covers : {2,18,4}*576, {6,6,4}*576a, {6,6,4}*576b, {2,6,12}*576a, {2,6,12}*576b
   7-fold covers : {2,6,28}*672b, {2,42,4}*672c
   8-fold covers : {2,12,8}*768c, {2,12,8}*768d, {4,12,4}*768e, {2,12,4}*768d, {4,6,4}*768c, {4,12,4}*768g, {2,6,8}*768d, {2,6,8}*768e, {2,6,4}*768a, {2,12,8}*768e, {2,12,8}*768f, {2,24,4}*768c, {2,24,4}*768d, {2,6,8}*768f, {2,12,8}*768g, {2,12,8}*768h, {8,6,4}*768a, {2,6,8}*768g, {4,6,8}*768b, {4,6,8}*768c, {2,6,4}*768b, {2,24,4}*768e, {2,12,4}*768e, {2,24,4}*768f, {8,6,4}*768f, {8,6,4}*768h, {4,6,4}*768k, {4,6,4}*768l
   9-fold covers : {2,54,4}*864c, {2,6,36}*864c, {6,18,4}*864e, {2,18,12}*864c, {2,6,12}*864d, {6,6,4}*864f, {6,6,12}*864h
   10-fold covers : {10,6,4}*960e, {2,6,20}*960c, {2,30,4}*960
   11-fold covers : {2,6,44}*1056b, {2,66,4}*1056c
   12-fold covers : {2,18,8}*1152a, {2,36,4}*1152b, {4,18,4}*1152a, {2,18,4}*1152b, {2,36,4}*1152c, {2,18,8}*1152b, {2,18,8}*1152c, {2,6,24}*1152a, {6,6,8}*1152a, {4,18,4}*1152e, {6,12,4}*1152e, {6,12,4}*1152f, {2,12,12}*1152d, {2,12,12}*1152e, {12,6,4}*1152a, {2,6,12}*1152b, {2,12,12}*1152h, {4,6,12}*1152b, {4,6,12}*1152c, {6,6,4}*1152c, {6,6,4}*1152d, {6,12,4}*1152g, {6,12,4}*1152h, {2,6,24}*1152b, {2,6,24}*1152c, {2,6,24}*1152d, {6,6,8}*1152b, {6,6,8}*1152c, {2,6,24}*1152e, {6,6,8}*1152d, {6,6,8}*1152e, {2,6,12}*1152f, {12,6,4}*1152d, {2,12,12}*1152j, {2,12,12}*1152l, {6,6,4}*1152h, {4,6,12}*1152g, {12,6,4}*1152h
   13-fold covers : {2,6,52}*1248b, {2,78,4}*1248c
   14-fold covers : {14,6,4}*1344, {2,6,28}*1344, {2,42,4}*1344
   15-fold covers : {2,18,20}*1440b, {2,90,4}*1440c, {6,6,20}*1440d, {6,30,4}*1440f, {2,30,12}*1440d, {2,6,60}*1440d
   17-fold covers : {2,6,68}*1632b, {2,102,4}*1632c
   18-fold covers : {2,54,4}*1728, {18,6,4}*1728, {2,6,36}*1728, {6,18,4}*1728a, {6,18,4}*1728b, {2,18,12}*1728a, {2,18,12}*1728b, {6,6,4}*1728a, {6,6,4}*1728b, {2,6,12}*1728a, {2,6,12}*1728b, {6,6,4}*1728c, {6,6,12}*1728a, {6,6,12}*1728b, {6,6,12}*1728c, {6,6,12}*1728d, {2,6,12}*1728c
   19-fold covers : {2,6,76}*1824b, {2,114,4}*1824c
   20-fold covers : {2,6,40}*1920a, {2,30,8}*1920a, {10,12,4}*1920b, {2,12,20}*1920b, {20,6,4}*1920a, {2,6,20}*1920a, {4,6,20}*1920b, {10,6,4}*1920b, {10,12,4}*1920c, {2,6,40}*1920b, {10,6,8}*1920a, {2,6,40}*1920c, {10,6,8}*1920b, {2,12,20}*1920c, {2,60,4}*1920b, {4,30,4}*1920a, {2,30,4}*1920b, {2,60,4}*1920c, {2,30,8}*1920b, {2,30,8}*1920c, {4,6,20}*1920d, {4,30,4}*1920e
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,6)(4,8);;
s2 := (3,4)(5,6)(7,8);;
s3 := (5,7);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s1*s2*s3*s1*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(8)!(1,2);
s1 := Sym(8)!(3,6)(4,8);
s2 := Sym(8)!(3,4)(5,6)(7,8);
s3 := Sym(8)!(5,7);
poly := sub<Sym(8)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s1*s2*s3*s1*s2*s3 >; 
 

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