Let $X$ be a CW-complex with 


* one 0-cell
* two 1-cells
* three 2-cells
* no cells in dimensions 3 or higher.


Is it always true that $\pi\_2(X)\ne 1$?



The second homotopy group of a simple CW-complex
There are classic examples, coming from [small cancellation theory](http://en.wikipedia.org/wiki/Small_cancellation_theory). See
the section of the Wikipedia article on asphericity. 


