A top-down view of the box, which I've rigged up to measure the seat still fits. It does, and in fact the depth of the box could be reduced by an inch to make it 15" by 14".
The seat back is reclined slightly, however, so beside the fact this it's nice and square there still remains wiggle room for fixing a back to the space-frame as per phone-box.
Were the box to be the full 45" high (allowing me a little head-room at full scale), then as it is 15" square then we can take as a rule-of-thumb that the box is three times as high as it is broad and deep... and I do like a good rule-of-thumb.
That's sufficient for the day though, and I need to mow the lawn.
