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Comment by A_D_E_P_T | Hacker News Reader

It's pretty egregious clickbait for Nature -- more along the lines of what I'd expect from Forbes or a similar outfit.

I mean, the title is saying that they "discovered" the "new class of shape" featured in this old kitchen tile: https://www.contemporist.com/reasons-why-you-should-get-crea...

Come on, now. The Egyptians, Greeks, and Romans were surely aware of it, and used similar pointed/curved and lenticular shapes in art and design.

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>Domokos and colleagues devised an algorithm for smoothly converting geometric tiles — either 2D polygons or 3D polyhedra, like the bubbles of a foam — into soft cells, and explored the range of possible shapes these rules permit. In 2D, the options are fairly limited: all tiles must have at least two cusp-like corners.

(Emphasis mine)

Am I reading that wrong or are the kitchen tiles in the images impossible based on the statement above

That shape has three cusp-like corners -- one at each sharp point, with smooth curves (convex/concave) between them. This satisfies the "at least two" condition.

The even simpler "lemon" is an even more egregious example, as it satisfies the conditions in two and three dimensions and yet is rather old and well-defined: https://mathworld.wolfram.com/LemonSurface.html

I think that tile shape has one cusp-like corner and two ~90-degree corners. Thus it's not a complete transformation of a polygon into a soft cell, and hence the "at least two" rule doesn't apply.

They aren't 90° corners -- and in any case it would be simple to modify the angle of those corners and keep the shape basically (or nearly) the same.

Also the plain 2D lemon/lozenge/lentil satisfies all conditions.

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