Polytope of Type {2,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,3}*72
if this polytope has a name.
Group : SmallGroup(72,46)
Rank : 4
Schlafli Type : {2,6,3}
Number of vertices, edges, etc : 2, 6, 9, 3
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,3,2} of size 144
   {2,6,3,4} of size 288
   {2,6,3,6} of size 432
   {2,6,3,4} of size 576
   {2,6,3,8} of size 1152
   {2,6,3,6} of size 1296
   {2,6,3,6} of size 1728
   {2,6,3,12} of size 1728
Vertex Figure Of :
   {2,2,6,3} of size 144
   {3,2,6,3} of size 216
   {4,2,6,3} of size 288
   {5,2,6,3} of size 360
   {6,2,6,3} of size 432
   {7,2,6,3} of size 504
   {8,2,6,3} of size 576
   {9,2,6,3} of size 648
   {10,2,6,3} of size 720
   {11,2,6,3} of size 792
   {12,2,6,3} of size 864
   {13,2,6,3} of size 936
   {14,2,6,3} of size 1008
   {15,2,6,3} of size 1080
   {16,2,6,3} of size 1152
   {17,2,6,3} of size 1224
   {18,2,6,3} of size 1296
   {19,2,6,3} of size 1368
   {20,2,6,3} of size 1440
   {21,2,6,3} of size 1512
   {22,2,6,3} of size 1584
   {23,2,6,3} of size 1656
   {24,2,6,3} of size 1728
   {25,2,6,3} of size 1800
   {26,2,6,3} of size 1872
   {27,2,6,3} of size 1944
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,6,3}*144, {2,6,6}*144b
   3-fold covers : {2,6,9}*216, {2,6,3}*216, {6,6,3}*216b
   4-fold covers : {8,6,3}*288, {2,6,12}*288b, {4,6,6}*288c, {2,12,6}*288c, {2,6,3}*288, {2,12,3}*288
   5-fold covers : {10,6,3}*360, {2,6,15}*360
   6-fold covers : {4,6,9}*432, {4,6,3}*432a, {2,6,18}*432b, {2,6,6}*432a, {12,6,3}*432b, {6,6,6}*432c, {2,6,6}*432d
   7-fold covers : {14,6,3}*504, {2,6,21}*504
   8-fold covers : {16,6,3}*576, {2,6,24}*576b, {2,12,12}*576b, {4,6,12}*576b, {8,6,6}*576c, {2,24,6}*576c, {4,12,6}*576c, {2,12,3}*576, {2,24,3}*576, {4,6,3}*576a, {4,12,3}*576, {2,6,6}*576a, {2,12,6}*576b
   9-fold covers : {2,18,9}*648, {2,6,9}*648a, {2,6,27}*648, {2,6,9}*648b, {2,6,9}*648c, {2,6,9}*648d, {2,6,3}*648, {2,18,3}*648, {6,6,9}*648b, {18,6,3}*648b, {6,6,3}*648c, {6,6,3}*648d, {6,6,3}*648e
   10-fold covers : {20,6,3}*720, {4,6,15}*720, {10,6,6}*720b, {2,30,6}*720a, {2,6,30}*720c
   11-fold covers : {22,6,3}*792, {2,6,33}*792
   12-fold covers : {8,6,9}*864, {8,6,3}*864a, {2,6,36}*864b, {2,6,12}*864a, {4,6,18}*864b, {2,12,18}*864b, {4,6,6}*864c, {2,12,6}*864c, {24,6,3}*864b, {2,6,9}*864, {2,12,9}*864, {2,6,3}*864, {2,12,3}*864, {6,6,12}*864c, {12,6,6}*864e, {2,6,12}*864g, {2,12,6}*864g, {4,6,6}*864h, {6,12,6}*864g, {6,6,3}*864, {6,12,3}*864b
   13-fold covers : {26,6,3}*936, {2,6,39}*936
   14-fold covers : {28,6,3}*1008, {4,6,21}*1008, {14,6,6}*1008b, {2,42,6}*1008a, {2,6,42}*1008c
   15-fold covers : {10,6,9}*1080, {10,6,3}*1080, {2,6,45}*1080, {2,6,15}*1080, {6,6,15}*1080b, {30,6,3}*1080b
   16-fold covers : {32,6,3}*1152, {4,12,12}*1152c, {4,24,6}*1152a, {8,12,6}*1152c, {2,12,24}*1152b, {2,24,12}*1152c, {4,24,6}*1152d, {8,12,6}*1152f, {2,12,24}*1152e, {2,24,12}*1152f, {4,12,6}*1152c, {2,12,12}*1152b, {8,6,12}*1152c, {4,6,24}*1152c, {16,6,6}*1152c, {2,48,6}*1152a, {2,6,48}*1152c, {2,6,3}*1152, {2,24,3}*1152, {4,6,3}*1152a, {4,12,3}*1152a, {8,6,3}*1152, {8,12,3}*1152, {4,12,3}*1152b, {4,24,3}*1152, {2,12,12}*1152g, {2,6,12}*1152a, {2,12,12}*1152i, {2,12,6}*1152c, {2,24,6}*1152b, {2,6,6}*1152a, {2,24,6}*1152d, {2,6,12}*1152d, {4,6,6}*1152f, {4,12,6}*1152j, {2,12,6}*1152e, {2,12,6}*1152f, {2,12,3}*1152, {4,6,3}*1152c, {2,6,6}*1152d
   17-fold covers : {34,6,3}*1224, {2,6,51}*1224
   18-fold covers : {4,18,9}*1296, {4,6,9}*1296a, {4,6,27}*1296, {4,6,9}*1296b, {4,6,9}*1296c, {4,6,9}*1296d, {4,6,3}*1296a, {4,18,3}*1296, {2,18,18}*1296b, {2,6,18}*1296a, {2,6,54}*1296b, {2,6,18}*1296c, {2,6,18}*1296d, {2,6,18}*1296e, {2,6,6}*1296c, {2,18,6}*1296h, {36,6,3}*1296b, {12,6,9}*1296b, {12,6,3}*1296c, {12,6,3}*1296d, {12,6,3}*1296e, {6,6,18}*1296c, {18,6,6}*1296c, {2,6,18}*1296i, {2,18,6}*1296i, {6,6,6}*1296f, {6,6,6}*1296k, {2,6,6}*1296e, {6,6,6}*1296n, {2,6,6}*1296f, {2,6,6}*1296g, {4,6,3}*1296b, {6,6,6}*1296q, {6,6,6}*1296r
   19-fold covers : {38,6,3}*1368, {2,6,57}*1368
   20-fold covers : {40,6,3}*1440, {8,6,15}*1440, {10,6,12}*1440b, {20,6,6}*1440c, {2,60,6}*1440a, {2,30,12}*1440a, {4,30,6}*1440a, {10,12,6}*1440c, {2,6,60}*1440c, {4,6,30}*1440c, {2,12,30}*1440c, {10,6,3}*1440, {10,12,3}*1440, {2,12,15}*1440, {2,6,15}*1440e
   21-fold covers : {14,6,9}*1512, {14,6,3}*1512, {2,6,63}*1512, {2,6,21}*1512, {6,6,21}*1512b, {42,6,3}*1512b
   22-fold covers : {44,6,3}*1584, {4,6,33}*1584, {22,6,6}*1584b, {2,66,6}*1584a, {2,6,66}*1584c
   23-fold covers : {46,6,3}*1656, {2,6,69}*1656
   24-fold covers : {16,6,9}*1728, {16,6,3}*1728a, {2,6,72}*1728b, {2,6,24}*1728a, {2,12,36}*1728b, {4,6,36}*1728b, {2,12,12}*1728b, {4,6,12}*1728b, {8,6,18}*1728b, {2,24,18}*1728b, {8,6,6}*1728c, {2,24,6}*1728c, {4,12,18}*1728b, {4,12,6}*1728c, {48,6,3}*1728b, {2,12,9}*1728, {4,6,9}*1728a, {2,24,9}*1728, {2,12,3}*1728, {2,24,3}*1728, {4,12,9}*1728, {4,6,3}*1728a, {4,12,3}*1728a, {6,6,24}*1728c, {24,6,6}*1728e, {2,6,24}*1728f, {2,24,6}*1728f, {12,6,12}*1728e, {6,12,12}*1728c, {6,24,6}*1728f, {8,6,6}*1728e, {2,12,12}*1728h, {4,12,6}*1728j, {12,12,6}*1728g, {4,6,12}*1728h, {2,6,18}*1728, {2,12,18}*1728b, {2,6,6}*1728b, {2,12,6}*1728a, {6,12,3}*1728, {6,24,3}*1728b, {12,6,3}*1728, {12,12,3}*1728b, {4,6,6}*1728c, {6,6,6}*1728a, {6,12,6}*1728f, {2,6,6}*1728c, {6,12,6}*1728j, {2,6,12}*1728c, {2,12,6}*1728c
   25-fold covers : {50,6,3}*1800, {2,6,75}*1800, {2,6,3}*1800, {2,30,3}*1800, {10,6,15}*1800, {2,30,15}*1800
   26-fold covers : {52,6,3}*1872, {4,6,39}*1872, {26,6,6}*1872b, {2,78,6}*1872a, {2,6,78}*1872c
   27-fold covers : {2,18,9}*1944a, {2,6,9}*1944a, {2,18,3}*1944a, {2,6,9}*1944b, {2,18,9}*1944b, {2,6,9}*1944c, {2,18,9}*1944c, {2,18,9}*1944d, {2,18,9}*1944e, {2,18,27}*1944, {2,6,27}*1944a, {2,6,9}*1944d, {2,18,9}*1944f, {2,18,9}*1944g, {2,18,9}*1944h, {2,18,9}*1944i, {2,6,9}*1944e, {2,18,9}*1944j, {2,6,27}*1944b, {2,6,27}*1944c, {2,6,81}*1944, {2,6,3}*1944, {2,18,3}*1944b, {6,18,9}*1944, {18,6,9}*1944b, {6,6,9}*1944c, {6,6,9}*1944d, {18,6,3}*1944c, {18,6,3}*1944d, {6,6,9}*1944e, {18,6,3}*1944e, {6,6,3}*1944b, {6,6,3}*1944c, {6,6,3}*1944d, {6,6,27}*1944b, {54,6,3}*1944b, {6,6,3}*1944e, {6,6,3}*1944f, {6,6,3}*1944g, {6,6,9}*1944f, {6,6,9}*1944g, {6,6,9}*1944h, {6,6,3}*1944h, {6,18,3}*1944
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 6, 7)( 8, 9)(10,11);;
s2 := ( 3, 6)( 4,10)( 5, 8)( 9,11);;
s3 := ( 3, 4)( 6, 9)( 7, 8)(10,11);;
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, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(11)!(1,2);
s1 := Sym(11)!( 6, 7)( 8, 9)(10,11);
s2 := Sym(11)!( 3, 6)( 4,10)( 5, 8)( 9,11);
s3 := Sym(11)!( 3, 4)( 6, 9)( 7, 8)(10,11);
poly := sub<Sym(11)|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, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 >;

to this polytope