### Reuleaux polygons (wheels, sewer lids, coins, etc.)

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Published on June 17, 2012

#### Description

Build working non-circular wheels with Reuleaux polygons. Make "safe" sewer hole covers. Print your own British 20 and 50 pence pieces!

Recall the smarty pants question about what shapes can be used for sewer hole covers? Circles and what else? You want a shape that has constant width: you don't want it to have an orientation at which it presents a narrower width and thus can pass through the opening it is covering. Well, one of the classes of shapes which work for sewer hole covers is Reuleaux polygons.

Reuleaux polygons are also used for coins such as the British 20 and 50 pence, Mauritian 10 rupee, and Jordanian quarter and half dinars.

For further information, see

en.wikipedia.org/wiki/Curve_of_constant_width
en.wikipedia.org/wiki/Reuleaux_triangle

P.S. I was prompted to post this when I saw the recent 5 Shekel coin posted, Thing #25051. While that coin is not a Reuleaux polygon owing to the even number of sides (nor does it claim to be), it reminded me of the coins which are.

P.P.S The rotor in a Wankel engine is not a Reuleaux triangle. Don't know why some Things which claim to be Wankel's are also tagged as Reuleaux. The sides of a Wankel are a little flatter which gives a little more volume for intake. (The shape of the sides of a Wankel are optimized for combustion ratio, not for being a constant width curve.)

#### Instructions

The reuleaux_polygon(n,w) module generates a Reuleaux polygon with n vertices and of constant width w centered at (0,0) in the XY-plane. The value of n must be a positive, odd integer >= 3.
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