Cylindrical square from a lathe tailstock.

[Toolmaker51]

DIYSwede, and Tony Foale; very clear you both familiar with geometry that makes Cylinder Squares dependable standards, whether comparison or direct measure.

To the General Population [inmates], I'll add three, carrying the process off in useful ways.
Brown & Sharpe [+ others] make a cylinder where ends vary intentionally. One end square isn't any surprise. Their 6" x 2"ish #558 product is OUT OF SQUARE on the other end! What? Yes, intentional! The exterior is marked with ellipses, interpolating out of squareness at given heights. Rotated in proximity with piece being inspected, the tilt goes from possible full contact to less than, regardless. Just as Tony demonstrated and DIYSwede observe, a cylinder [tilted] has two [minimum] perpendicular lines of contact. The #558 can relay needed correction quite accurately; greater angles are likely planned and better verified by sine tools.

Another fine square, especially popular setting up in accordance with horizontal [vertical plane] locations is the Magnetic Cylinder. Constructing one wouldn't be out of range for many private shops. They are non-magnetic stainless with epoxied Nd magnets [usually 3] with a small gap less than flush from the base. The broad base supports the smaller cylinder readily, as they are machined one piece. Careful handling would make brass, bronze or aluminum rather acceptable.

Finally, pic might disclose a rarity, the cloverleaf square.

Some tools arise out of utility.
Some tools born out of imagination; may not gain interest outside that realm.
Some go away when processes get outmoded.
Some disappear, thankfully. We call those gimmicks.

https://www.google.com/search?q=brow...w=1600&bih=736
https://www.google.com/search?client...4dUDCAY&uact=5