Polytope of Type {3,4,2}

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

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