Polytope of Type {18,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,2,2}*144
if this polytope has a name.
Group : SmallGroup(144,112)
Rank : 4
Schlafli Type : {18,2,2}
Number of vertices, edges, etc : 18, 18, 2, 2
Order of s0s1s2s3 : 18
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{18,2,2,2} of size 288
{18,2,2,3} of size 432
{18,2,2,4} of size 576
{18,2,2,5} of size 720
{18,2,2,6} of size 864
{18,2,2,7} of size 1008
{18,2,2,8} of size 1152
{18,2,2,9} of size 1296
{18,2,2,10} of size 1440
{18,2,2,11} of size 1584
{18,2,2,12} of size 1728
{18,2,2,13} of size 1872
Vertex Figure Of :
{2,18,2,2} of size 288
{4,18,2,2} of size 576
{4,18,2,2} of size 576
{4,18,2,2} of size 576
{6,18,2,2} of size 864
{6,18,2,2} of size 864
{8,18,2,2} of size 1152
{4,18,2,2} of size 1152
{9,18,2,2} of size 1296
{6,18,2,2} of size 1296
{6,18,2,2} of size 1296
{3,18,2,2} of size 1296
{6,18,2,2} of size 1296
{10,18,2,2} of size 1440
{12,18,2,2} of size 1728
{12,18,2,2} of size 1728
{12,18,2,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {9,2,2}*72
3-fold quotients : {6,2,2}*48
6-fold quotients : {3,2,2}*24
9-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {36,2,2}*288, {18,2,4}*288, {18,4,2}*288a
3-fold covers : {54,2,2}*432, {18,2,6}*432, {18,6,2}*432a, {18,6,2}*432b
4-fold covers : {36,4,2}*576a, {36,2,4}*576, {18,4,4}*576, {72,2,2}*576, {18,2,8}*576, {18,8,2}*576, {18,4,2}*576
5-fold covers : {18,2,10}*720, {18,10,2}*720, {90,2,2}*720
6-fold covers : {108,2,2}*864, {54,2,4}*864, {54,4,2}*864a, {36,2,6}*864, {36,6,2}*864a, {36,6,2}*864b, {18,2,12}*864, {18,12,2}*864a, {18,4,6}*864, {18,6,4}*864a, {18,6,4}*864b, {18,12,2}*864b
7-fold covers : {18,2,14}*1008, {18,14,2}*1008, {126,2,2}*1008
8-fold covers : {36,4,4}*1152, {18,4,8}*1152a, {18,8,4}*1152a, {36,8,2}*1152a, {72,4,2}*1152a, {18,4,8}*1152b, {18,8,4}*1152b, {36,8,2}*1152b, {72,4,2}*1152b, {18,4,4}*1152a, {36,4,2}*1152a, {36,2,8}*1152, {72,2,4}*1152, {18,2,16}*1152, {18,16,2}*1152, {144,2,2}*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
9-fold covers : {162,2,2}*1296, {18,2,18}*1296, {18,18,2}*1296a, {18,18,2}*1296c, {18,6,6}*1296a, {18,6,2}*1296a, {18,6,2}*1296b, {54,2,6}*1296, {54,6,2}*1296a, {54,6,2}*1296b, {18,6,6}*1296b, {18,6,6}*1296c, {18,6,6}*1296d, {18,6,6}*1296e, {18,6,2}*1296i
10-fold covers : {36,2,10}*1440, {36,10,2}*1440, {18,2,20}*1440, {18,20,2}*1440a, {18,4,10}*1440, {18,10,4}*1440, {180,2,2}*1440, {90,2,4}*1440, {90,4,2}*1440a
11-fold covers : {18,2,22}*1584, {18,22,2}*1584, {198,2,2}*1584
12-fold covers : {108,4,2}*1728a, {108,2,4}*1728, {54,4,4}*1728, {216,2,2}*1728, {54,2,8}*1728, {54,8,2}*1728, {36,2,12}*1728, {36,6,4}*1728a, {18,4,12}*1728, {18,12,4}*1728a, {36,4,6}*1728, {72,2,6}*1728, {72,6,2}*1728a, {72,6,2}*1728b, {18,2,24}*1728, {18,24,2}*1728a, {18,6,8}*1728a, {18,8,6}*1728, {36,12,2}*1728a, {36,12,2}*1728b, {36,6,4}*1728b, {18,6,8}*1728b, {18,24,2}*1728b, {18,12,4}*1728b, {54,4,2}*1728, {18,4,6}*1728a, {18,6,4}*1728, {18,6,6}*1728, {18,6,2}*1728, {36,6,2}*1728, {18,4,6}*1728b, {18,12,2}*1728a, {18,12,2}*1728b
13-fold covers : {18,2,26}*1872, {18,26,2}*1872, {234,2,2}*1872
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,18);;
s2 := (19,20);;
s3 := (21,22);;
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,
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(22)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);
s1 := Sym(22)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,18);
s2 := Sym(22)!(19,20);
s3 := Sym(22)!(21,22);
poly := sub<Sym(22)|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, s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope