Really fell in love with this pull down menu that slides as you pull down further. Design was rejected by the client, but I'm still a big fan of the navigation.

With this style navigation bar, it doesn't take up space when not in use. This leaves room for the content to surface to the top and focus all of the user's attention. 

Pull down from the top to reveal the navigation bar. The current screen is highlighted in the middle with other available screens to the right and left.

Keep pulling down to cycle through the available icons. As a new screen comes into the center it will highlight. Let go of the screen and it will snap to that selection to change screens.