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A razor I traded away is this remarkable folding razor Bigelow-Parkin. Barely larger than a blade, with two small extrusions to hold it, this thing shaved remarkably well.
There's a
The trick is to lock your wrist and use your lower arm as a giant handle.
For shaving under the nose tilt razor slightly between thumb and index finger, then lock wrist again.
There is another patent for a single edge, adjustable version. Unfortunately, it was never made:
View from the top with the little grip handles folded in. Note the star-shaped holes - they give more grip than round ones or handles without holes would.
The handles fold out:
View from the bottom. You open the razor by lifting the base plate where it says Open here:
Then you put a blade in ...
close the base plate and fold out the handles fully. Pick up the razor with thumb and index finger and you're ready to go.