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Is it a curve of constant width like the 20p and 50p? If its sides are straight it cannot be. Also from wiki: > The new design is intended to make counterfeit

Is it a curve of constant width like the 20p and 50p? If its sides are straight it cannot be. Also from wiki: > The new design is intended to make counterfeiting more difficult, via an undisclosed hidden security feature, called 'iSIS' (Integrated Secure Identification Systems). [1] Huh. [1]: https://en.wikipedia.org/wiki/One_pound_(British_coin) https://en.wikipedia.org/wiki/One_pound_(British_coin)

_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 ago
  But with an even number of sides (12 in the new coin), can that work?
  - _archon_ 10y ago
    It 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 ago
  No, it's twelve-sided, therefore cannot be.
nerfhammer 10y ago
> Is it a curve of constant width like the 20p and 50p? If its sides are straight it cannot be. If I'm not mistaken it has to have an odd number of sides, but it has 12. The sides looks like they might be very slightly curved in order to facilitate rolling. But it not being of constant width could still make life more difficult for vending machines etc.

_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 ago
But with an even number of sides (12 in the new coin), can that work?
- _archon_ 10y ago
  It 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 ago
No, it's twelve-sided, therefore cannot be.

nerfhammer 10y ago

> Is it a curve of constant width like the 20p and 50p? If its sides are straight it cannot be. If I'm not mistaken it has to have an odd number of sides, but it has 12. The sides looks like they might be very slightly curved in order to facilitate rolling. But it not being of constant width could still make life more difficult for vending machines etc.