Polytope of Type {16,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,2,2}*128
if this polytope has a name.
Group : SmallGroup(128,2140)
Rank : 4
Schlafli Type : {16,2,2}
Number of vertices, edges, etc : 16, 16, 2, 2
Order of s0s1s2s3 : 16
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{16,2,2,2} of size 256
{16,2,2,3} of size 384
{16,2,2,4} of size 512
{16,2,2,5} of size 640
{16,2,2,6} of size 768
{16,2,2,7} of size 896
{16,2,2,9} of size 1152
{16,2,2,10} of size 1280
{16,2,2,11} of size 1408
{16,2,2,13} of size 1664
{16,2,2,14} of size 1792
{16,2,2,15} of size 1920
Vertex Figure Of :
{2,16,2,2} of size 256
{4,16,2,2} of size 512
{4,16,2,2} of size 512
{6,16,2,2} of size 768
{10,16,2,2} of size 1280
{14,16,2,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8,2,2}*64
4-fold quotients : {4,2,2}*32
8-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {16,4,2}*256a, {16,2,4}*256, {32,2,2}*256
3-fold covers : {48,2,2}*384, {16,2,6}*384, {16,6,2}*384
4-fold covers : {16,4,2}*512a, {16,8,2}*512c, {16,8,2}*512d, {16,4,4}*512a, {32,4,2}*512a, {32,4,2}*512b, {64,2,2}*512
5-fold covers : {80,2,2}*640, {16,2,10}*640, {16,10,2}*640
6-fold covers : {16,4,6}*768a, {16,12,2}*768a, {48,4,2}*768a, {16,6,4}*768a, {16,2,12}*768, {48,2,4}*768, {32,2,6}*768, {32,6,2}*768, {96,2,2}*768
7-fold covers : {112,2,2}*896, {16,2,14}*896, {16,14,2}*896
9-fold covers : {16,2,18}*1152, {16,18,2}*1152, {144,2,2}*1152, {16,6,6}*1152a, {16,6,6}*1152b, {16,6,6}*1152c, {48,6,2}*1152a, {48,2,6}*1152, {48,6,2}*1152b, {48,6,2}*1152c, {16,6,2}*1152
10-fold covers : {16,4,10}*1280a, {16,20,2}*1280a, {80,4,2}*1280a, {16,10,4}*1280, {16,2,20}*1280, {80,2,4}*1280, {32,2,10}*1280, {32,10,2}*1280, {160,2,2}*1280
11-fold covers : {16,2,22}*1408, {16,22,2}*1408, {176,2,2}*1408
13-fold covers : {16,2,26}*1664, {16,26,2}*1664, {208,2,2}*1664
14-fold covers : {16,4,14}*1792a, {16,28,2}*1792a, {112,4,2}*1792a, {16,14,4}*1792, {16,2,28}*1792, {112,2,4}*1792, {32,2,14}*1792, {32,14,2}*1792, {224,2,2}*1792
15-fold covers : {16,2,30}*1920, {16,30,2}*1920, {240,2,2}*1920, {16,6,10}*1920, {16,10,6}*1920, {48,2,10}*1920, {48,10,2}*1920, {80,2,6}*1920, {80,6,2}*1920
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
s2 := (17,18);;
s3 := (19,20);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(20)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);
s1 := Sym(20)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);
s2 := Sym(20)!(17,18);
s3 := Sym(20)!(19,20);
poly := sub<Sym(20)|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 >;
to this polytope