16 Apr
2014
16 Apr
'14
2:40 a.m.
On 4/15/14, Adam P. Goucher <apgoucher@gmx.com> wrote:
Oh, sorry, I didn't see that you needed it to be an embedding. It can't be embedded on the torus, since it has 36 vertices, 144 edges and an Euler characteristic of at most:
36 - 144 + 96 = -12
So, if you are to embed it on a surface without crossings, you'll need to have at least seven holes.
Whoa! ... where does your 96 come from? WFL
There are 144 edges. The maximum number of faces is achieved when every face is a triangle, in which case there are (2/3).144 = 96 triangles. Sincerely, Adam P. Goucher