Formula to create a Reuleaux polygon The Wikipedia articles for Reuleaux triangle and curve of constant width do a good job of describing the properties of a Reuleaux polygon, but they don't give a straightforward formula for computing or drawing such a figure, except in terms of the manual compass-and-straightedge construction.
Is there a formula or algorithm that, given the number of sides and the width/diameter, would give some data representation of a Reuleaux polygon that could be used to recreate it programmatically?
In particular, I'm looking for the coordinates of the vertices (or the angle/direction from one vertex to another) and the details of the arc connecting them.

As you can see from the diagram below, if $L$ is the length of a side of the regular polygon, $n$ (odd) the number of its sides and $W$ its width, then:
$$L=2W\sin{\pi\over 2n}.$$

