Re: [math-fun] late follow-up

On 12/16/06, Fred lunnon <fred.lunnon@gmail.com> wrote:

Two exceptions, having a common tetrahedron, with edges in natural order, are

[6, 5, 4, 4, 5, 2, 4, 4, 3, 2] [6, 5, 4, 4, 5, 2, 6, 3, 4, 4]

These looked a good bet for gluing together to form a rational 3-flat 6-tope; alas, the 15-th side turns out to be sqrt(40/7)!

But I failed to take inot account that the second simplex might alternatively be written [6, 5, 4, 4, 5, 2, 3, 6, 4, 4] Gluing this on to the first instead gives a rational 3-flat 6-tope with edges [in alphabetic order of vertices] [6, 5, 4, 4, 5, 2, 3, 6, 4, 4, 4, 4, 3, 2, 5] Fred Lunnon