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I'm just thinking of a way to get a bigger screen without a bigger device. (isn't that what everybody would like?) :D

The home button could be on the side, but I think we'll all agree that wouldn't be a nice place for it.
 
This it a bit out there too, but what about having no home button... instead you could double tap the screen with two fingers or something.
 
What About The Sensors?

If the whole front of the iphone was a screen, then there would be no room for the sensors on the front, as well as the home button. This would make the rumored front-facing camera for video chat impossible along with the ambient light sensor and the proximity sensor impossible to have because the screen would be in the way.

As much as I like the fact of a larger screen, it wouldn't work without increasing the size of the iPhone.
 
For both practically and aesthetic purposes, the home button as it is now is perfect.

Anyway, In my opinion, a physical button doesn't fully support Apple's idea of the 'future being touch'. There would be no harm with making it a touch button as manual hardware resets could still be achieved. Additionally, I think it could be a 'touch/click' button similar to the click-wheel design we have today, i.e. touching it does one function, pressing it does another. This way it opens up the software to perform more versatile actions. Also, it'd be an nice touch if the square outline image on the home button was illuminated and maybe pulsed when it was sleeping like the computers do. This will give it a nice futuristic edge and of course makes it fully operational at night time which it currently isn't.
 
I just though of a way to work around the home button and sensors problem.

To go to the home screen, you could just slide your finger across the bottom of the screen. This would not interfere with the application, because no application currently has this as a way to control them. If the iPhone crashed, you could hold one sleep/wake button along with one volume button for 6-10 seconds to shut down the device.

Also, Apple could integrate the ambient light sensor and the proximity sensor into the screen. Didn't I see a patent for this awhile ago?
 
I think it could be a 'touch/click' button similar to the click-wheel design we have today, i.e. touching it does one function, pressing it does another. This way it opens up the software to perform more versatile actions. Also, it'd be an nice touch if the square outline image on the home button was illuminated and maybe pulsed when it was sleeping like the computers do. This will give it a nice futuristic edge and of course makes it fully operational at night time which it currently isn't.

I like this.

Clearly you must have been a design major. :D
 
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