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Polytope of Type {2,4,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,3}*48
if this polytope has a name.
Group : SmallGroup(48,48)
Rank : 4
Schlafli Type : {2,4,3}
Number of vertices, edges, etc : 2, 4, 6, 3
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,3,2} of size 96
   {2,4,3,4} of size 192
   {2,4,3,6} of size 288
   {2,4,3,4} of size 384
   {2,4,3,8} of size 768
   {2,4,3,6} of size 864
   {2,4,3,6} of size 1152
   {2,4,3,12} of size 1152
Vertex Figure Of :
   {2,2,4,3} of size 96
   {3,2,4,3} of size 144
   {4,2,4,3} of size 192
   {5,2,4,3} of size 240
   {6,2,4,3} of size 288
   {7,2,4,3} of size 336
   {8,2,4,3} of size 384
   {9,2,4,3} of size 432
   {10,2,4,3} of size 480
   {11,2,4,3} of size 528
   {12,2,4,3} of size 576
   {13,2,4,3} of size 624
   {14,2,4,3} of size 672
   {15,2,4,3} of size 720
   {16,2,4,3} of size 768
   {17,2,4,3} of size 816
   {18,2,4,3} of size 864
   {19,2,4,3} of size 912
   {20,2,4,3} of size 960
   {21,2,4,3} of size 1008
   {22,2,4,3} of size 1056
   {23,2,4,3} of size 1104
   {24,2,4,3} of size 1152
   {25,2,4,3} of size 1200
   {26,2,4,3} of size 1248
   {27,2,4,3} of size 1296
   {28,2,4,3} of size 1344
   {29,2,4,3} of size 1392
   {30,2,4,3} of size 1440
   {31,2,4,3} of size 1488
   {33,2,4,3} of size 1584
   {34,2,4,3} of size 1632
   {35,2,4,3} of size 1680
   {36,2,4,3} of size 1728
   {37,2,4,3} of size 1776
   {38,2,4,3} of size 1824
   {39,2,4,3} of size 1872
   {40,2,4,3} of size 1920
   {41,2,4,3} of size 1968
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   3-fold covers : {2,4,9}*144
   4-fold covers : {4,4,3}*192a, {2,4,12}*192b, {2,4,12}*192c, {4,4,3}*192b, {2,8,3}*192, {2,4,6}*192
   5-fold covers : {2,4,15}*240
   6-fold covers : {2,4,9}*288, {2,4,18}*288b, {2,4,18}*288c, {6,4,3}*288, {2,12,3}*288, {2,12,6}*288d
   7-fold covers : {2,4,21}*336
   8-fold covers : {4,4,3}*384a, {4,4,3}*384b, {4,4,6}*384b, {2,4,6}*384a, {4,4,6}*384c, {2,8,3}*384, {2,8,6}*384a, {4,8,3}*384, {2,4,24}*384c, {2,4,24}*384d, {8,4,3}*384, {2,4,12}*384b, {4,4,6}*384d, {2,4,6}*384b, {2,4,12}*384c, {2,8,6}*384b, {2,8,6}*384c
   9-fold covers : {2,4,27}*432
   10-fold covers : {10,4,3}*480, {2,20,6}*480b, {2,4,15}*480, {2,4,30}*480b, {2,4,30}*480c
   11-fold covers : {2,4,33}*528
   12-fold covers : {4,4,9}*576a, {2,4,36}*576b, {2,4,36}*576c, {4,4,9}*576b, {2,8,9}*576, {2,4,18}*576, {12,4,3}*576, {2,24,3}*576, {6,8,3}*576, {4,12,3}*576, {6,4,6}*576a, {2,12,6}*576a, {2,12,6}*576b
   13-fold covers : {2,4,39}*624
   14-fold covers : {14,4,3}*672, {2,28,6}*672b, {2,4,21}*672, {2,4,42}*672b, {2,4,42}*672c
   15-fold covers : {2,4,45}*720
   16-fold covers : {8,4,3}*768a, {8,4,3}*768b, {2,8,3}*768, {2,8,6}*768a, {2,8,12}*768c, {2,8,12}*768d, {4,8,3}*768a, {4,8,3}*768b, {8,8,3}*768, {2,4,12}*768b, {2,4,12}*768c, {4,4,3}*768a, {4,4,6}*768b, {4,4,12}*768c, {4,4,12}*768d, {4,8,3}*768c, {4,8,3}*768d, {4,4,3}*768b, {4,4,6}*768c, {4,4,6}*768d, {2,8,6}*768b, {2,8,6}*768c, {4,4,3}*768c, {4,8,3}*768e, {4,8,3}*768f, {2,4,48}*768c, {2,4,48}*768d, {16,4,3}*768, {2,4,12}*768d, {4,4,6}*768e, {4,4,12}*768e, {4,4,12}*768f, {2,8,6}*768d, {2,8,6}*768e, {4,4,6}*768f, {2,4,6}*768a, {2,8,12}*768e, {2,8,12}*768f, {2,4,24}*768c, {2,4,24}*768d, {4,8,6}*768c, {2,8,6}*768f, {2,8,12}*768g, {2,8,12}*768h, {8,4,6}*768c, {2,8,6}*768g, {4,8,6}*768d, {2,4,6}*768b, {2,4,24}*768e, {2,4,12}*768e, {2,4,24}*768f
   17-fold covers : {2,4,51}*816
   18-fold covers : {2,4,27}*864, {2,4,54}*864b, {2,4,54}*864c, {18,4,3}*864, {2,36,6}*864c, {6,4,9}*864, {2,12,9}*864, {2,12,18}*864c, {2,12,3}*864, {2,12,6}*864d, {6,12,3}*864a, {6,12,3}*864b, {6,12,6}*864h
   19-fold covers : {2,4,57}*912
   20-fold covers : {4,4,15}*960a, {20,4,3}*960, {10,8,3}*960, {2,4,60}*960b, {2,4,60}*960c, {4,4,15}*960b, {2,8,15}*960, {10,4,6}*960, {2,20,6}*960c, {2,4,30}*960
   21-fold covers : {2,4,63}*1008
   22-fold covers : {22,4,3}*1056, {2,44,6}*1056b, {2,4,33}*1056, {2,4,66}*1056b, {2,4,66}*1056c
   23-fold covers : {2,4,69}*1104
   24-fold covers : {4,4,9}*1152a, {4,4,9}*1152b, {4,4,18}*1152b, {2,4,18}*1152a, {4,4,18}*1152c, {2,8,9}*1152, {2,8,18}*1152a, {4,8,9}*1152, {2,4,72}*1152c, {2,4,72}*1152d, {8,4,9}*1152, {2,4,36}*1152b, {4,4,18}*1152d, {2,4,18}*1152b, {2,4,36}*1152c, {2,8,18}*1152b, {2,8,18}*1152c, {2,24,3}*1152, {2,24,6}*1152a, {12,8,3}*1152, {4,12,3}*1152a, {4,12,6}*1152d, {12,4,3}*1152, {6,8,3}*1152, {24,4,3}*1152, {8,12,3}*1152, {4,24,3}*1152, {6,4,12}*1152b, {2,12,12}*1152f, {2,12,12}*1152g, {12,4,6}*1152c, {2,12,6}*1152b, {2,12,12}*1152i, {4,12,6}*1152g, {6,4,6}*1152a, {6,4,12}*1152d, {2,24,6}*1152b, {2,24,6}*1152c, {2,24,6}*1152d, {6,8,6}*1152a, {2,24,6}*1152e, {6,8,6}*1152c, {4,12,6}*1152j, {2,12,6}*1152f, {2,12,12}*1152k, {4,12,6}*1152l, {2,12,3}*1152, {2,12,12}*1152l, {6,12,6}*1152f
   25-fold covers : {2,4,75}*1200
   26-fold covers : {26,4,3}*1248, {2,52,6}*1248b, {2,4,39}*1248, {2,4,78}*1248b, {2,4,78}*1248c
   27-fold covers : {2,4,81}*1296, {6,4,3}*1296b, {2,4,9}*1296, {2,12,3}*1296, {2,12,9}*1296a, {2,12,9}*1296b
   28-fold covers : {4,4,21}*1344a, {28,4,3}*1344, {14,8,3}*1344, {2,4,84}*1344b, {2,4,84}*1344c, {4,4,21}*1344b, {2,8,21}*1344, {14,4,6}*1344, {2,28,6}*1344, {2,4,42}*1344
   29-fold covers : {2,4,87}*1392
   30-fold covers : {10,4,9}*1440, {2,20,18}*1440b, {2,4,45}*1440, {2,4,90}*1440b, {2,4,90}*1440c, {10,12,3}*1440, {6,4,15}*1440, {2,12,15}*1440, {2,12,30}*1440d, {30,4,3}*1440, {2,60,6}*1440d
   31-fold covers : {2,4,93}*1488
   33-fold covers : {2,4,99}*1584
   34-fold covers : {34,4,3}*1632, {2,68,6}*1632b, {2,4,51}*1632, {2,4,102}*1632b, {2,4,102}*1632c
   35-fold covers : {2,4,105}*1680
   36-fold covers : {4,4,27}*1728a, {2,4,108}*1728b, {2,4,108}*1728c, {4,4,27}*1728b, {2,8,27}*1728, {2,4,54}*1728, {36,4,3}*1728, {18,8,3}*1728, {12,4,9}*1728, {12,12,3}*1728a, {2,24,9}*1728, {2,24,3}*1728, {6,8,9}*1728, {6,24,3}*1728a, {4,12,9}*1728, {4,12,3}*1728a, {18,4,6}*1728a, {2,36,6}*1728, {6,4,18}*1728b, {2,12,18}*1728a, {2,12,18}*1728b, {6,12,6}*1728a, {2,12,6}*1728a, {2,12,6}*1728b, {6,24,3}*1728b, {12,12,3}*1728b, {4,12,3}*1728b, {2,12,12}*1728o, {6,12,6}*1728e, {6,12,6}*1728f, {6,12,6}*1728g, {6,12,6}*1728h, {2,12,6}*1728c
   37-fold covers : {2,4,111}*1776
   38-fold covers : {38,4,3}*1824, {2,76,6}*1824b, {2,4,57}*1824, {2,4,114}*1824b, {2,4,114}*1824c
   39-fold covers : {2,4,117}*1872
   40-fold covers : {4,4,15}*1920a, {2,40,6}*1920a, {20,8,3}*1920, {4,20,6}*1920b, {20,4,3}*1920, {10,8,3}*1920, {40,4,3}*1920, {4,4,15}*1920b, {4,4,30}*1920b, {2,4,30}*1920a, {4,4,30}*1920c, {2,8,15}*1920a, {2,8,30}*1920a, {4,8,15}*1920, {2,4,120}*1920c, {2,4,120}*1920d, {8,4,15}*1920, {10,4,12}*1920b, {2,20,12}*1920b, {20,4,6}*1920b, {2,20,6}*1920a, {4,20,6}*1920c, {10,4,6}*1920, {10,4,12}*1920c, {2,40,6}*1920b, {10,8,6}*1920a, {2,40,6}*1920c, {10,8,6}*1920b, {2,20,12}*1920c, {2,4,60}*1920b, {4,4,30}*1920d, {2,4,30}*1920b, {2,4,60}*1920c, {2,8,30}*1920b, {2,8,30}*1920c
   41-fold covers : {2,4,123}*1968
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4)(5,6);;
s2 := (4,5);;
s3 := (5,6);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(6)!(1,2);
s1 := Sym(6)!(3,4)(5,6);
s2 := Sym(6)!(4,5);
s3 := Sym(6)!(5,6);
poly := sub<Sym(6)|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, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2 >; 
 

to this polytope