Polytope of Type {6,3,2}

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

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

Permutation Representation (Magma) :

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

to this polytope