Is there any thing composed of elementary particles in this world that is not 3 dimensional? Is there any thing composed of elementary particles in this world that is not 3 dimensional? I know that there is graphite which is singular atom thick. Is there anything in this world that has no depth? So I guess what I am asking is there an object that does not have volume  
 A: If by object you mean something composed of elementary particles then there are no two dimensional objects due to the uncertainty principle.
If we take the direction normal to the surface to be the $z$ axis then the uncertainty principle tells us that:
$$ \sigma_z \sigma_{p_z} \ge \frac{\hbar}{2} $$
for an object to become two dimension would require $\sigma_z \rightarrow 0$ and that implies $\sigma_{p_z} \rightarrow \infty$ and therefore requires infinite energy.
However there are many examples of systems that are approximately two dimensional. Graphene would be a good example.
Even if you're willing to relax the requirement for the object to be something physical then I'm still not sure anything can be truly two dimensional. The example that springs to mind is an event horizon, but this is a classical concept and quantum gravity effects may well blur it into a region of finite volume. I suspect quantum mechanics will forbid anything from being truly two dimensional.
A: Coastlines, for example. Coastline of Great Britain has fractal dimension of 1.25.
Source:
https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension
