Polytope of Type {4,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,6}*96
if this polytope has a name.
Group : SmallGroup(96,209)
Rank : 4
Schlafli Type : {4,2,6}
Number of vertices, edges, etc : 4, 4, 6, 6
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,2,6,2} of size 192
   {4,2,6,3} of size 288
   {4,2,6,4} of size 384
   {4,2,6,3} of size 384
   {4,2,6,4} of size 384
   {4,2,6,4} of size 384
   {4,2,6,4} of size 576
   {4,2,6,6} of size 576
   {4,2,6,6} of size 576
   {4,2,6,6} of size 576
   {4,2,6,8} of size 768
   {4,2,6,4} of size 768
   {4,2,6,6} of size 768
   {4,2,6,9} of size 864
   {4,2,6,3} of size 864
   {4,2,6,6} of size 864
   {4,2,6,4} of size 960
   {4,2,6,5} of size 960
   {4,2,6,6} of size 960
   {4,2,6,5} of size 960
   {4,2,6,5} of size 960
   {4,2,6,10} of size 960
   {4,2,6,12} of size 1152
   {4,2,6,12} of size 1152
   {4,2,6,12} of size 1152
   {4,2,6,4} of size 1152
   {4,2,6,3} of size 1152
   {4,2,6,12} of size 1152
   {4,2,6,14} of size 1344
   {4,2,6,15} of size 1440
   {4,2,6,4} of size 1728
   {4,2,6,12} of size 1728
   {4,2,6,12} of size 1728
   {4,2,6,18} of size 1728
   {4,2,6,18} of size 1728
   {4,2,6,6} of size 1728
   {4,2,6,6} of size 1728
   {4,2,6,6} of size 1728
   {4,2,6,12} of size 1728
   {4,2,6,6} of size 1728
   {4,2,6,20} of size 1920
   {4,2,6,15} of size 1920
   {4,2,6,20} of size 1920
   {4,2,6,4} of size 1920
   {4,2,6,4} of size 1920
   {4,2,6,4} of size 1920
   {4,2,6,5} of size 1920
   {4,2,6,6} of size 1920
   {4,2,6,6} of size 1920
   {4,2,6,6} of size 1920
   {4,2,6,10} of size 1920
   {4,2,6,10} of size 1920
   {4,2,6,5} of size 1920
   {4,2,6,10} of size 1920
   {4,2,6,10} of size 1920
   {4,2,6,10} of size 1920
   {4,2,6,10} of size 1920
Vertex Figure Of :
   {2,4,2,6} of size 192
   {3,4,2,6} of size 288
   {4,4,2,6} of size 384
   {6,4,2,6} of size 576
   {3,4,2,6} of size 576
   {6,4,2,6} of size 576
   {6,4,2,6} of size 576
   {8,4,2,6} of size 768
   {8,4,2,6} of size 768
   {4,4,2,6} of size 768
   {9,4,2,6} of size 864
   {4,4,2,6} of size 864
   {6,4,2,6} of size 864
   {10,4,2,6} of size 960
   {12,4,2,6} of size 1152
   {12,4,2,6} of size 1152
   {12,4,2,6} of size 1152
   {6,4,2,6} of size 1152
   {14,4,2,6} of size 1344
   {5,4,2,6} of size 1440
   {6,4,2,6} of size 1440
   {15,4,2,6} of size 1440
   {18,4,2,6} of size 1728
   {9,4,2,6} of size 1728
   {18,4,2,6} of size 1728
   {18,4,2,6} of size 1728
   {4,4,2,6} of size 1728
   {6,4,2,6} of size 1728
   {20,4,2,6} of size 1920
   {5,4,2,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,3}*48, {2,2,6}*48
   3-fold quotients : {4,2,2}*32
   4-fold quotients : {2,2,3}*24
   6-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,12}*192, {4,4,6}*192, {8,2,6}*192
   3-fold covers : {4,2,18}*288, {12,2,6}*288, {4,6,6}*288a, {4,6,6}*288c
   4-fold covers : {4,4,12}*384, {4,2,24}*384, {8,2,12}*384, {4,8,6}*384a, {8,4,6}*384a, {4,8,6}*384b, {8,4,6}*384b, {4,4,6}*384a, {16,2,6}*384, {4,4,6}*384d
   5-fold covers : {20,2,6}*480, {4,10,6}*480, {4,2,30}*480
   6-fold covers : {4,2,36}*576, {4,4,18}*576, {8,2,18}*576, {12,2,12}*576, {4,12,6}*576a, {12,4,6}*576, {4,6,12}*576a, {24,2,6}*576, {8,6,6}*576a, {4,6,12}*576b, {8,6,6}*576c, {4,12,6}*576c
   7-fold covers : {28,2,6}*672, {4,14,6}*672, {4,2,42}*672
   8-fold covers : {4,8,6}*768a, {8,4,6}*768a, {8,8,6}*768a, {8,8,6}*768b, {8,8,6}*768c, {8,8,6}*768d, {8,2,24}*768, {8,4,12}*768a, {4,4,24}*768a, {8,4,12}*768b, {4,4,24}*768b, {4,8,12}*768a, {4,4,12}*768a, {4,4,12}*768b, {4,8,12}*768b, {4,8,12}*768c, {4,8,12}*768d, {4,16,6}*768a, {16,4,6}*768a, {4,16,6}*768b, {16,4,6}*768b, {4,4,6}*768a, {4,8,6}*768b, {8,4,6}*768b, {16,2,12}*768, {4,2,48}*768, {32,2,6}*768, {4,4,6}*768e, {4,4,12}*768e, {4,4,12}*768f, {4,8,6}*768c, {8,4,6}*768c, {4,8,6}*768d
   9-fold covers : {4,2,54}*864, {36,2,6}*864, {12,2,18}*864, {12,6,6}*864a, {4,6,18}*864a, {4,18,6}*864a, {4,6,6}*864b, {4,6,18}*864b, {4,6,6}*864c, {12,6,6}*864b, {12,6,6}*864d, {12,6,6}*864e, {4,6,6}*864h, {12,6,6}*864f, {4,6,6}*864j, {4,6,6}*864k
   10-fold covers : {20,2,12}*960, {4,20,6}*960, {20,4,6}*960, {4,10,12}*960, {40,2,6}*960, {8,10,6}*960, {4,2,60}*960, {4,4,30}*960, {8,2,30}*960
   11-fold covers : {44,2,6}*1056, {4,22,6}*1056, {4,2,66}*1056
   12-fold covers : {4,4,36}*1152, {4,12,12}*1152b, {4,12,12}*1152c, {12,4,12}*1152, {4,8,18}*1152a, {8,4,18}*1152a, {8,12,6}*1152b, {12,8,6}*1152a, {4,24,6}*1152a, {8,12,6}*1152c, {4,24,6}*1152c, {24,4,6}*1152a, {4,8,18}*1152b, {8,4,18}*1152b, {8,12,6}*1152e, {12,8,6}*1152b, {4,24,6}*1152d, {8,12,6}*1152f, {4,24,6}*1152f, {24,4,6}*1152b, {4,4,18}*1152a, {4,12,6}*1152b, {12,4,6}*1152a, {4,12,6}*1152c, {8,2,36}*1152, {4,2,72}*1152, {8,6,12}*1152b, {8,6,12}*1152c, {4,6,24}*1152b, {4,6,24}*1152c, {12,2,24}*1152, {24,2,12}*1152, {16,2,18}*1152, {16,6,6}*1152a, {16,6,6}*1152c, {48,2,6}*1152, {4,4,18}*1152d, {12,4,6}*1152b, {12,4,6}*1152c, {4,6,6}*1152d, {4,6,12}*1152b, {4,12,6}*1152g, {12,6,6}*1152b, {4,6,6}*1152f, {4,12,6}*1152j
   13-fold covers : {52,2,6}*1248, {4,26,6}*1248, {4,2,78}*1248
   14-fold covers : {28,2,12}*1344, {4,14,12}*1344, {4,28,6}*1344, {28,4,6}*1344, {56,2,6}*1344, {8,14,6}*1344, {4,2,84}*1344, {4,4,42}*1344, {8,2,42}*1344
   15-fold covers : {20,2,18}*1440, {4,10,18}*1440, {4,2,90}*1440, {12,10,6}*1440, {20,6,6}*1440a, {20,6,6}*1440c, {4,30,6}*1440a, {12,2,30}*1440, {60,2,6}*1440, {4,6,30}*1440b, {4,30,6}*1440b, {4,6,30}*1440c
   17-fold covers : {68,2,6}*1632, {4,34,6}*1632, {4,2,102}*1632
   18-fold covers : {4,2,108}*1728, {4,4,54}*1728, {8,2,54}*1728, {12,2,36}*1728, {36,2,12}*1728, {12,6,12}*1728a, {4,6,36}*1728a, {4,18,12}*1728a, {4,12,18}*1728a, {12,4,18}*1728, {4,36,6}*1728a, {36,4,6}*1728, {4,6,12}*1728a, {4,12,6}*1728b, {12,12,6}*1728a, {72,2,6}*1728, {24,2,18}*1728, {24,6,6}*1728a, {8,6,18}*1728a, {8,18,6}*1728a, {8,6,6}*1728b, {4,6,36}*1728b, {4,6,12}*1728b, {8,6,18}*1728b, {8,6,6}*1728c, {4,12,18}*1728b, {4,12,6}*1728c, {24,6,6}*1728b, {24,6,6}*1728d, {24,6,6}*1728e, {12,6,12}*1728b, {12,6,12}*1728c, {12,6,12}*1728e, {12,6,12}*1728f, {12,12,6}*1728b, {12,12,6}*1728c, {12,12,6}*1728f, {8,6,6}*1728e, {24,6,6}*1728f, {4,12,6}*1728j, {12,12,6}*1728g, {4,6,12}*1728h, {8,6,6}*1728f, {4,6,12}*1728k, {4,6,12}*1728l, {8,6,6}*1728g, {4,4,6}*1728b, {4,4,6}*1728c, {4,12,6}*1728n, {4,12,6}*1728o, {12,4,6}*1728b, {4,4,12}*1728c, {4,6,12}*1728n
   19-fold covers : {76,2,6}*1824, {4,38,6}*1824, {4,2,114}*1824
   20-fold covers : {4,4,60}*1920, {4,20,12}*1920, {20,4,12}*1920, {4,8,30}*1920a, {8,4,30}*1920a, {8,20,6}*1920a, {20,8,6}*1920a, {4,40,6}*1920a, {40,4,6}*1920a, {4,8,30}*1920b, {8,4,30}*1920b, {8,20,6}*1920b, {20,8,6}*1920b, {4,40,6}*1920b, {40,4,6}*1920b, {4,4,30}*1920a, {4,20,6}*1920a, {20,4,6}*1920a, {8,2,60}*1920, {4,2,120}*1920, {8,10,12}*1920, {4,10,24}*1920, {40,2,12}*1920, {20,2,24}*1920, {16,2,30}*1920, {16,10,6}*1920, {80,2,6}*1920, {20,4,6}*1920b, {4,20,6}*1920c, {4,4,30}*1920d
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)( 9,10);;
s3 := ( 5, 9)( 6, 7)( 8,10);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(10)!(2,3);
s1 := Sym(10)!(1,2)(3,4);
s2 := Sym(10)!( 7, 8)( 9,10);
s3 := Sym(10)!( 5, 9)( 6, 7)( 8,10);
poly := sub<Sym(10)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope