Polytope of Type {3,4,2,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,4,2,8}*384
if this polytope has a name.
Group : SmallGroup(384,18032)
Rank : 5
Schlafli Type : {3,4,2,8}
Number of vertices, edges, etc : 3, 6, 4, 8, 8
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,4,2,8,2} of size 768
Vertex Figure Of :
{2,3,4,2,8} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,4,2,4}*192
4-fold quotients : {3,4,2,2}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,4,2,16}*768, {3,4,2,8}*768, {6,4,2,8}*768b, {6,4,2,8}*768c
3-fold covers : {9,4,2,8}*1152, {3,4,2,24}*1152
5-fold covers : {3,4,2,40}*1920, {15,4,2,8}*1920
Permutation Representation (GAP) :
s0 := (3,4);;
s1 := (2,3);;
s2 := (1,2)(3,4);;
s3 := ( 6, 7)( 8, 9)(10,11);;
s4 := ( 5, 6)( 7, 8)( 9,10)(11,12);;
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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s0*s2*s1*s0*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(12)!(3,4);
s1 := Sym(12)!(2,3);
s2 := Sym(12)!(1,2)(3,4);
s3 := Sym(12)!( 6, 7)( 8, 9)(10,11);
s4 := Sym(12)!( 5, 6)( 7, 8)( 9,10)(11,12);
poly := sub<Sym(12)|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, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s2*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope