Im surprised not to find a radians-based clock among these.

Represent the minute component with an imaginary number, so you can tell it apart from the hour... you know, for clarity of course heheheh. I think you'd have to apply the same transform that the 360 degree clock gets in the article, where (1) and (2π) are at the top and adding runs clockwise.

"It's i till 2π... oh yeah sorry, that's what we call 3π/2:-1-i around here."