How to arrange mirrors so I can't see myself? If I wanted to surround myself with mirrors how would I need to arrange them so that if I stood in the middle of them I couldn't see myself in any reflection? 
For simplicity let's just say we only do the sides, not the ceiling and the floor. 
How many panels would I need and in what configuration? 
It seems to me that only a star formation could work, where all the mirrors are angled slightly outwards from me, but I'm not sure that at some point I would be reflected.
Is this even possible? Any ideas?
UPDATE:
Based on all the responses below I believe the problem is that I cannot have any angle facing me that is at 180 degrees or less.
For example, this is at about a 30 degree angle and doesn't work (thanks @mmesser314):

And this one is exactly 180 degrees and obviously will not work:

But from 181 degrees onward light is reflected away, like this:

So if we could figure out a configuration where I cannot see any angle that is less than 180 degrees I should never be able to see my reflection. This is what I came up with. Can anyone tell me if this (or some variation of it) seems valid?

 A: This would work, but you might think it is cheating.

If there can be no gaps, I would guess it is not possible. Your star idea won't work. Light that leaves you will bounce up the V and back out. The ray shown misses you. But if you look at a fan of rays, some will go to the left of you and some to the right. There is always one that will hit you. 

If you use a smooth curve instead of planar mirrors, you cannot avoid seeing at least a point. This shows a ray that goes to the left and another that goes to the right. Some ray in between will hit you. 

You might try to avoid it by putting mirror in the way to block that ray. But that piece has the same problem. 

You might try to make a mirror where all the rays are deflected to the left. But that is a spiral, not a closed curve. 
A: Here I'll show that in 3d configuration, it is impossible. However the argument could be adapted to 2d also, if we used 2d black-body radiation instead.
The proof is by contradiction, using thermodynamic arguments. Assume there exists some finite solid angle in which direction you wouldn't see yourself. Now this would imply that if you send light in this direction from your eye, it never reflects back to your body and never gets absorbed. Suppose now that your body (including your eye) is perfectly black, and it has a constant temperature $T$. Then some of the radiation emitted from your eye will never come back, implying it remains in the chamber. As more and more radiation will be compressed in the room, the radiation intensity at least at some place must diverge to infinity. This could be used to heat a hotter body with a colder one. Contradiction.
A: Unless you use methods that you might consider cheating, it's almost certainly impossible.  The reason why is that the Law of Reflection states that $\theta_i=\theta_r$.  This means, in words that when a ray of light hits a reflective surface the angle that the ray of light makes with the surface before it hits (the incident angle, or $\theta_i$) is equal to the angle that the ray of light makes with the surface after it is reflected (the reflected angle, $\theta_r$).  Out of convention, these angles are measured normal to the surface of the mirror. The diagram below shows reflection of a ray of light at some arbitrary angle.  

Here's the kicker though:  If the ray of light hits normal to the surface (perpendicular to the surface, then $\theta=0$, so the ray of light reflects straight back, retracing its path.  In this thought experiment of yours, any ray of light that leaves your body and strikes a mirror normal to the surface like this will be seen my you.  (More or less.  I am treating you as a point particle, rather than a person with dimensions.  This is ok because seeing your own eyes still counts as seeing you).  
So now let's view the last paragraph in the negative.  In order to not see yourself, there can not be a single ray of light that leaves your head and strikes a mirror perpendicularly.  Try to imagnine being in a room that satisfies that criteria. A mirror sphere wouldn't work.  A mirror cylinder wouldn't work. A regular polygon won't work.  Even if you try to imagine some spiky, star shaped wall of mirrors, I believe the vertices still would likely act as corner reflectors.  Unless I'm missing a shape really, really outside the box, the answer is no.
