Polytope of Type {8,4,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,2}*128a
if this polytope has a name.
Group : SmallGroup(128,1728)
Rank : 4
Schlafli Type : {8,4,2}
Number of vertices, edges, etc : 8, 16, 4, 2
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{8,4,2,2} of size 256
{8,4,2,3} of size 384
{8,4,2,5} of size 640
{8,4,2,6} of size 768
{8,4,2,7} of size 896
{8,4,2,9} of size 1152
{8,4,2,10} of size 1280
{8,4,2,11} of size 1408
{8,4,2,13} of size 1664
{8,4,2,14} of size 1792
{8,4,2,15} of size 1920
Vertex Figure Of :
{2,8,4,2} of size 256
{4,8,4,2} of size 512
{4,8,4,2} of size 512
{6,8,4,2} of size 768
{3,8,4,2} of size 768
{10,8,4,2} of size 1280
{14,8,4,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,4,2}*64, {8,2,2}*64
4-fold quotients : {2,4,2}*32, {4,2,2}*32
8-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,4,2}*256a, {8,8,2}*256b, {8,8,2}*256c, {8,4,4}*256a, {16,4,2}*256a, {16,4,2}*256b
3-fold covers : {24,4,2}*384a, {8,12,2}*384a, {8,4,6}*384a
4-fold covers : {8,8,2}*512a, {8,4,8}*512b, {8,8,4}*512a, {8,4,4}*512a, {8,8,4}*512c, {8,8,4}*512e, {8,8,4}*512g, {8,4,4}*512b, {8,4,8}*512c, {8,4,2}*512a, {8,8,2}*512d, {16,4,2}*512a, {16,4,2}*512b, {8,16,2}*512a, {8,16,2}*512b, {8,16,2}*512d, {16,8,2}*512c, {16,8,2}*512d, {8,16,2}*512f, {16,8,2}*512e, {16,8,2}*512f, {16,4,4}*512a, {16,4,4}*512b, {32,4,2}*512a, {32,4,2}*512b
5-fold covers : {40,4,2}*640a, {8,20,2}*640a, {8,4,10}*640a
6-fold covers : {8,4,6}*768a, {8,12,2}*768a, {24,4,2}*768a, {8,8,6}*768b, {8,8,6}*768c, {8,24,2}*768a, {8,24,2}*768c, {24,8,2}*768b, {24,8,2}*768c, {8,4,12}*768a, {8,12,4}*768a, {24,4,4}*768a, {16,4,6}*768a, {16,12,2}*768a, {48,4,2}*768a, {16,4,6}*768b, {16,12,2}*768b, {48,4,2}*768b
7-fold covers : {56,4,2}*896a, {8,28,2}*896a, {8,4,14}*896a
9-fold covers : {8,4,18}*1152a, {8,36,2}*1152a, {72,4,2}*1152a, {8,12,6}*1152a, {8,12,6}*1152b, {8,12,6}*1152c, {24,4,6}*1152a, {24,12,2}*1152a, {24,12,2}*1152b, {24,12,2}*1152c, {8,4,6}*1152a, {8,4,2}*1152a, {24,4,2}*1152a, {8,12,2}*1152a
10-fold covers : {8,4,10}*1280a, {8,20,2}*1280a, {40,4,2}*1280a, {8,8,10}*1280b, {8,8,10}*1280c, {8,40,2}*1280a, {8,40,2}*1280c, {40,8,2}*1280b, {40,8,2}*1280c, {8,4,20}*1280a, {8,20,4}*1280a, {40,4,4}*1280a, {16,4,10}*1280a, {16,20,2}*1280a, {80,4,2}*1280a, {16,4,10}*1280b, {16,20,2}*1280b, {80,4,2}*1280b
11-fold covers : {8,4,22}*1408a, {8,44,2}*1408a, {88,4,2}*1408a
13-fold covers : {8,4,26}*1664a, {8,52,2}*1664a, {104,4,2}*1664a
14-fold covers : {8,4,14}*1792a, {8,28,2}*1792a, {56,4,2}*1792a, {8,8,14}*1792b, {8,8,14}*1792c, {8,56,2}*1792a, {8,56,2}*1792c, {56,8,2}*1792b, {56,8,2}*1792c, {8,4,28}*1792a, {8,28,4}*1792a, {56,4,4}*1792a, {16,4,14}*1792a, {16,28,2}*1792a, {112,4,2}*1792a, {16,4,14}*1792b, {16,28,2}*1792b, {112,4,2}*1792b
15-fold covers : {8,4,30}*1920a, {8,60,2}*1920a, {120,4,2}*1920a, {8,12,10}*1920a, {8,20,6}*1920a, {24,4,10}*1920a, {40,4,6}*1920a, {40,12,2}*1920a, {24,20,2}*1920a
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 6)( 5, 8)( 9,11)(10,12)(13,15);;
s1 := ( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,10)(11,13)(12,14)(15,16);;
s2 := ( 2, 4)( 3, 6)(10,13)(12,15);;
s3 := (17,18);;
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,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
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, 6)( 5, 8)( 9,11)(10,12)(13,15);
s1 := Sym(18)!( 1, 2)( 3, 5)( 4, 7)( 6, 9)( 8,10)(11,13)(12,14)(15,16);
s2 := Sym(18)!( 2, 4)( 3, 6)(10,13)(12,15);
s3 := Sym(18)!(17,18);
poly := sub<Sym(18)|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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope