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Polytope of Type {2,4,2,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,2,8}*256
if this polytope has a name.
Group : SmallGroup(256,54027)
Rank : 5
Schlafli Type : {2,4,2,8}
Number of vertices, edges, etc : 2, 4, 4, 8, 8
Order of s0s1s2s3s4 : 8
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,4,2,8,2} of size 512
Vertex Figure Of :
{2,2,4,2,8} of size 512
{3,2,4,2,8} of size 768
{5,2,4,2,8} of size 1280
{7,2,4,2,8} of size 1792
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,4,2,4}*128, {2,2,2,8}*128
4-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
8-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,8,2,8}*512, {2,4,4,8}*512b, {2,4,2,16}*512
3-fold covers : {6,4,2,8}*768a, {2,4,6,8}*768a, {2,12,2,8}*768, {2,4,2,24}*768
5-fold covers : {10,4,2,8}*1280, {2,4,10,8}*1280, {2,20,2,8}*1280, {2,4,2,40}*1280
7-fold covers : {14,4,2,8}*1792, {2,4,14,8}*1792, {2,28,2,8}*1792, {2,4,2,56}*1792
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4)(5,6);;
s3 := ( 8, 9)(10,11)(12,13);;
s4 := ( 7, 8)( 9,10)(11,12)(13,14);;
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*s1*s0*s1,
s0*s2*s0*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, s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(14)!(1,2);
s1 := Sym(14)!(4,5);
s2 := Sym(14)!(3,4)(5,6);
s3 := Sym(14)!( 8, 9)(10,11)(12,13);
s4 := Sym(14)!( 7, 8)( 9,10)(11,12)(13,14);
poly := sub<Sym(14)|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*s1*s0*s1, s0*s2*s0*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,
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope