Polytope of Type {12,2,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,2,2,2}*192
if this polytope has a name.
Group : SmallGroup(192,1512)
Rank : 5
Schlafli Type : {12,2,2,2}
Number of vertices, edges, etc : 12, 12, 2, 2, 2
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{12,2,2,2,2} of size 384
{12,2,2,2,3} of size 576
{12,2,2,2,4} of size 768
{12,2,2,2,5} of size 960
{12,2,2,2,6} of size 1152
{12,2,2,2,7} of size 1344
{12,2,2,2,9} of size 1728
{12,2,2,2,10} of size 1920
Vertex Figure Of :
{2,12,2,2,2} of size 384
{4,12,2,2,2} of size 768
{4,12,2,2,2} of size 768
{4,12,2,2,2} of size 768
{3,12,2,2,2} of size 768
{6,12,2,2,2} of size 1152
{6,12,2,2,2} of size 1152
{6,12,2,2,2} of size 1152
{3,12,2,2,2} of size 1152
{6,12,2,2,2} of size 1152
{4,12,2,2,2} of size 1728
{6,12,2,2,2} of size 1728
{6,12,2,2,2} of size 1728
{6,12,2,2,2} of size 1728
{10,12,2,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,2,2,2}*96
3-fold quotients : {4,2,2,2}*64
4-fold quotients : {3,2,2,2}*48
6-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,4,2,2}*384a, {12,2,2,4}*384, {12,2,4,2}*384, {24,2,2,2}*384
3-fold covers : {36,2,2,2}*576, {12,2,2,6}*576, {12,2,6,2}*576, {12,6,2,2}*576a, {12,6,2,2}*576b
4-fold covers : {12,4,4,2}*768, {12,2,4,4}*768, {12,4,2,4}*768a, {12,8,2,2}*768a, {24,4,2,2}*768a, {12,8,2,2}*768b, {24,4,2,2}*768b, {12,4,2,2}*768a, {12,2,2,8}*768, {12,2,8,2}*768, {24,2,2,4}*768, {24,2,4,2}*768, {48,2,2,2}*768, {12,4,2,2}*768b
5-fold covers : {12,2,2,10}*960, {12,2,10,2}*960, {12,10,2,2}*960, {60,2,2,2}*960
6-fold covers : {36,4,2,2}*1152a, {12,4,2,6}*1152a, {12,4,6,2}*1152, {12,12,2,2}*1152a, {12,12,2,2}*1152c, {36,2,2,4}*1152, {36,2,4,2}*1152, {12,2,4,6}*1152a, {12,2,6,4}*1152a, {12,6,2,4}*1152b, {12,6,2,4}*1152c, {12,6,4,2}*1152b, {12,6,4,2}*1152c, {12,2,2,12}*1152, {12,2,12,2}*1152, {72,2,2,2}*1152, {24,2,2,6}*1152, {24,2,6,2}*1152, {24,6,2,2}*1152b, {24,6,2,2}*1152c
7-fold covers : {12,2,2,14}*1344, {12,2,14,2}*1344, {12,14,2,2}*1344, {84,2,2,2}*1344
9-fold covers : {108,2,2,2}*1728, {12,2,2,18}*1728, {12,2,18,2}*1728, {12,18,2,2}*1728a, {36,2,2,6}*1728, {36,2,6,2}*1728, {36,6,2,2}*1728a, {36,6,2,2}*1728b, {12,6,2,2}*1728a, {12,6,2,2}*1728b, {12,6,6,2}*1728a, {12,2,6,6}*1728a, {12,2,6,6}*1728b, {12,2,6,6}*1728c, {12,6,2,6}*1728a, {12,6,2,6}*1728b, {12,6,6,2}*1728b, {12,6,6,2}*1728c, {12,6,6,2}*1728d, {12,6,2,2}*1728g, {12,6,6,2}*1728e, {12,6,2,2}*1728i
10-fold covers : {60,4,2,2}*1920a, {12,4,2,10}*1920a, {12,4,10,2}*1920, {12,20,2,2}*1920, {60,2,2,4}*1920, {60,2,4,2}*1920, {12,2,4,10}*1920, {12,2,10,4}*1920, {12,10,2,4}*1920, {12,10,4,2}*1920, {12,2,2,20}*1920, {12,2,20,2}*1920, {120,2,2,2}*1920, {24,2,2,10}*1920, {24,2,10,2}*1920, {24,10,2,2}*1920
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);;
s1 := ( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);;
s2 := (13,14);;
s3 := (15,16);;
s4 := (17,18);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, 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(18)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(18)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(18)!(13,14);
s3 := Sym(18)!(15,16);
s4 := Sym(18)!(17,18);
poly := sub<Sym(18)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, 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