For a constant angular speed watch, if you want some specific figures being placed at the corners, you have to adjust the aspect ratio of the dial rectangle.

A Graphics to begin with:

Manipulate[
    {
                    Dashed, GrayLevel[.7], 
                    InfiniteLine[{0, 0}, Through[{Cos, Sin}[π/6 #]]],
                    Dashing[{}], Black, Thick, 
                    InfiniteLine[{0, 0}, Through[{Cos, Sin}[π/12 + π/6 #]]]
                    } &amp; /@ Range[0, 5] //
        Graphics[{#,
                    EdgeForm[{Black, Thick}], FaceForm[White],
                    Rectangle[##] &amp; @@ (1/
                                2 {{-1, 1}, (Tan[π/6] + ε) {-1, 
                                                1}})
                    },
                PlotRange -&gt; {{-1, 1}, (Tan[π/6] + ε) {-1, 1}},
                Frame -&gt; True, FrameStyle -&gt; Thick, FrameTicks -&gt; None] &amp;,
    {{ε, 0}, -0.5, 10}]




With a proper grid, you can then use the transformation method from other answers to fill in good-looking figures.

Around the Clock
I've heard that halogen headlights should be replaced in pairs.  I've been wondering if the same is true of HID headlights.  They are much more expensive, so I would like to avoid having to buy two of them if one will suffice.
