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Polytope of Type {3,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,2}*96
if this polytope has a name.
Group : SmallGroup(96,226)
Rank : 4
Schlafli Type : {3,6,2}
Number of vertices, edges, etc : 4, 12, 8, 2
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,6,2,2} of size 192
   {3,6,2,3} of size 288
   {3,6,2,4} of size 384
   {3,6,2,5} of size 480
   {3,6,2,6} of size 576
   {3,6,2,7} of size 672
   {3,6,2,8} of size 768
   {3,6,2,9} of size 864
   {3,6,2,10} of size 960
   {3,6,2,11} of size 1056
   {3,6,2,12} of size 1152
   {3,6,2,13} of size 1248
   {3,6,2,14} of size 1344
   {3,6,2,15} of size 1440
   {3,6,2,17} of size 1632
   {3,6,2,18} of size 1728
   {3,6,2,19} of size 1824
   {3,6,2,20} of size 1920
Vertex Figure Of :
   {2,3,6,2} of size 192
   {3,3,6,2} of size 480
   {4,3,6,2} of size 768
   {4,3,6,2} of size 768
   {6,3,6,2} of size 960
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,3,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,6,4}*192, {3,12,2}*192, {6,6,2}*192
   3-fold covers : {3,6,6}*288, {3,6,2}*288
   4-fold covers : {3,6,4}*384b, {3,6,2}*384, {3,12,4}*384, {3,6,8}*384, {6,6,4}*384, {6,12,2}*384a, {12,6,2}*384a, {6,12,2}*384b, {12,6,2}*384b, {6,6,2}*384b
   5-fold covers : {3,6,10}*480, {15,6,2}*480
   6-fold covers : {3,6,12}*576, {3,12,2}*576, {3,12,6}*576, {3,6,4}*576a, {6,6,6}*576b, {6,6,2}*576a, {6,6,2}*576b
   7-fold covers : {3,6,14}*672, {21,6,2}*672
   8-fold covers : {3,12,2}*768, {3,12,4}*768a, {3,12,4}*768b, {3,12,8}*768, {3,6,4}*768a, {3,6,4}*768b, {3,6,4}*768c, {6,6,4}*768a, {3,6,4}*768d, {3,12,4}*768c, {3,12,4}*768d, {3,6,16}*768, {12,12,2}*768a, {6,12,4}*768a, {12,6,4}*768a, {6,6,2}*768c, {6,6,2}*768d, {6,6,4}*768d, {6,6,2}*768e, {12,12,2}*768b, {6,12,4}*768b, {6,12,2}*768, {12,6,2}*768, {12,12,2}*768c, {12,12,2}*768d, {6,6,8}*768, {6,24,2}*768a, {24,6,2}*768a, {6,6,4}*768e, {12,6,4}*768b, {6,24,2}*768b, {24,6,2}*768b
   9-fold covers : {3,6,18}*864, {9,6,2}*864, {3,6,2}*864, {3,6,6}*864
   10-fold covers : {3,6,20}*960, {15,12,2}*960, {3,12,10}*960, {15,6,4}*960, {6,6,10}*960, {6,30,2}*960, {30,6,2}*960
   11-fold covers : {3,6,22}*1056, {33,6,2}*1056
   12-fold covers : {3,6,2}*1152, {3,12,12}*1152, {3,6,4}*1152a, {3,6,12}*1152, {3,6,6}*1152, {3,6,24}*1152, {3,6,8}*1152, {3,12,4}*1152b, {6,6,12}*1152a, {6,12,2}*1152a, {12,6,2}*1152a, {6,6,4}*1152e, {6,12,6}*1152b, {12,6,6}*1152b, {6,12,2}*1152c, {12,6,2}*1152c, {6,6,2}*1152a, {6,6,2}*1152b, {6,12,6}*1152d, {12,6,6}*1152c, {6,12,2}*1152d, {12,6,2}*1152d, {6,6,6}*1152b, {6,6,4}*1152f, {6,12,2}*1152e, {12,6,2}*1152e, {3,12,2}*1152
   13-fold covers : {3,6,26}*1248, {39,6,2}*1248
   14-fold covers : {3,6,28}*1344, {21,12,2}*1344, {3,12,14}*1344, {21,6,4}*1344, {6,6,14}*1344, {6,42,2}*1344, {42,6,2}*1344
   15-fold covers : {3,6,10}*1440, {15,6,6}*1440, {3,6,30}*1440, {15,6,2}*1440e
   17-fold covers : {3,6,34}*1632, {51,6,2}*1632
   18-fold covers : {3,6,36}*1728, {9,12,2}*1728, {3,12,18}*1728, {9,6,4}*1728a, {3,12,2}*1728, {3,6,4}*1728a, {6,6,18}*1728, {6,18,2}*1728, {18,6,2}*1728, {6,6,2}*1728a, {6,6,2}*1728b, {3,12,6}*1728, {3,6,12}*1728, {6,6,6}*1728d, {6,6,6}*1728e, {6,6,6}*1728f, {6,6,2}*1728c
   19-fold covers : {3,6,38}*1824, {57,6,2}*1824
   20-fold covers : {15,6,2}*1920, {3,12,20}*1920, {3,6,20}*1920, {15,6,4}*1920, {3,6,10}*1920, {3,6,40}*1920, {15,6,8}*1920, {15,12,4}*1920, {6,6,20}*1920, {6,60,2}*1920a, {60,6,2}*1920a, {6,12,10}*1920a, {6,30,4}*1920, {12,6,10}*1920a, {12,30,2}*1920a, {30,12,2}*1920a, {6,30,2}*1920, {30,6,2}*1920, {6,12,10}*1920b, {12,6,10}*1920b, {6,60,2}*1920b, {60,6,2}*1920b, {6,6,10}*1920, {30,6,4}*1920, {12,30,2}*1920b, {30,12,2}*1920b
Permutation Representation (GAP) :
s0 := (1,4)(2,6);;
s1 := (3,4)(5,6);;
s2 := (1,4)(2,6)(3,5);;
s3 := (7,8);;
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, 
s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(8)!(1,4)(2,6);
s1 := Sym(8)!(3,4)(5,6);
s2 := Sym(8)!(1,4)(2,6)(3,5);
s3 := Sym(8)!(7,8);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >; 
 

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