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The coin does appear to be a Reuleaux solid, which was a relief to me. British coins are some of the most common Reuleaux solids in the world. The sides are no
by _archon_ 10y ago
The coin does appear to be a Reuleaux solid, which was a relief to me. British coins are some of the most common Reuleaux solids in the world.
The sides are not straight; they are curved outwards. The curve is defined by an arc of a circle whose center is the opposite corner on the coin.
It's a neat class of shapes! My dive into them came while researching the rotary Wankel engine (rotors are roughly Reuleaux triangles)
- chiph 10y agoBut with an even number of sides (12 in the new coin), can that work?
- _archon_ 10y agoIt can not. Reuleaux solids must have an odd number of vertices, or they indeed don't work. It would appear that I didn't have my brain fully on this morning. To apply the principle of Reuleaux geometry to a regular shape with an even number of vertices, you'd make arcs tangent to the point in question, extending in a curve that increases the coin's diameter as the arc gets longer. The arc would come to an end in a point midway to the next point, where it would intersect with that point's arc. You'd have a star-shaped solid where all geometry external to the inscribed circle are tapered triangles. Kind of neat, but it would be tough to put through a vending machine.
- deleted 10y ago[deleted]
- grkvlt 10y agoNo, it's twelve-sided, therefore cannot be.