I guess this is correct.

来源: 于 2009-03-04 17:50:00 [博客] [旧帖] [给我悄悄话] 本文已被阅读：次

Basically using Euler's formula, V-E+F=1, where F=2005.
Besides the four corners, every vertex is of degree at least 3, so we have 8+3(V-4) ≤ 2E. Combine these two, we get the answer.