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First, the natural thing to do is to single-click the AirPort base station. If you do, you'll see something like this.
Image #1. Single click on base station icon.
You may, at first, think that the next thing to do is to click the Edit button. But not so fast. Some useful information can be displayed if you hover the mouse cursor over each of the wireless client names. If you do, you'll see something like that shown below. The IP address, Hardware address, and some performance information about the connection will be revealed.
Image #2. Hovering mouse cursor over wrieless client
So far, so good. Now you can go ahead and click the Edit button, and you'll see the familiar configuration tabs: Base Station, Internet, Wireless, and so on.
Image #3
But here's a nice trick, and it's a product of Macintosh Rule #4: Always See What Happens When You Try: Option + click (or Option + double-click). [I made that rule up, but it's true.*]
In this case, if you Option + click the base station, nothing happens. However, if you Option + double-click the base station, you'll take an instant shortcut to all the data you saw before, but in a floating window.
Image #4. Option + double-click brings up a new Summary tab.
A new Summary tab on the upper left has all of the the information you had in Image #2 above and more. Plus it's easier to take a compact screen shot. Compare that to the standard window if you had merely clicked the Edit button. (Image #3.)
Instead of hovering over a device name, now you have disclosure triangles that show the same information about each wireless client: Connection, Data rate, IP address and so on.
Image #5. Closeup of Wireless Clients window.
That there are two different ways to reveal all this information is interesting. That the second way is mildly hidden for those who don't think to Option + double-click is also interesting.
One More Thing
With the Airport Utility, it's all too easy to focus on the devices that appear in the home window. For example, you can also click or Option + double-click the Internet globe. But don't forget that this app also has formal Preferences that may be of interest. Don't overlook those.
AirPort Utility 6 isn't the most comprehensive Wi-Fi management tool that Apple could have built. There are still some features missing compared to version 5.6, but it's also being slowly refined and improved. That's nice to see.
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* Thanks to TMO's Adam Christianson for discovering the Option + double-click trick.