When one uses a Nikon DX (APS-C) camera on an FX camera body, the camera automatically enters a "DX crop mode", using only the center portion of the sensor to match the DX format, as explained on Nikon's web site.
The FX format is roughly 36×24mm, while DX is 24×16mm, and it's this smaller size that DX crop mode uses. Notice that the short edge of the FX format is equal to the long edge of DX — and of course the image circle is perfectly round, not oblong. Do any Nikon full-frame cameras allow a "square DX" format, either 24×24mm (with some possible vignetting in the extreme corners) or slightly reduced?