Pairs of Packable Scutoids

Pairs of Packable Scutoids

Pairs of Packable Scutoids 628 472 mathgrrl

There’s a new shape in town!

In a new article Scutoids are a geometrical solution to three-dimensional packing of epithelia in the journal Nature, a group of scientists just introduced a new shape that they have dubbed a “Scutoid”.

To make a 3D model of this new shape, we created a simple “polyloft” module in OpenSCAD that lofts from one polygon to another.  This enabled us to transition from a pentagon to a hexagon (with an extra point in the middle) to construct a scutoid shape. Here is the code for the polygonal lofter, since I’m sure we’ll need to use it for something else in the future!

```module polyloft(A,B){

/// DEFINE POINTS //////////////////////////////////////////////

// points at kth level
function points(k) = [ for(i=[0:len(A)-1]) go(A[i],B[i],k/steps) ];

// recursively list all points up to level n
function allpoints(n) = (n==0 ? points(0) : concat(allpoints(n-1),points(n)));

// all points
// listed ccz starting with bottom slice and going up
allpoints = allpoints(steps+1);

/// DEFINE FACES ///////////////////////////////////////////////

for(i=[0:len(A)-1])
[ i+(k-1)*len(A),(i+1)%len(A)+(k-1)*len(A),
(i+1)%len(A)+len(A)+(k-1)*len(A),
i+len(A)+(k-1)*len(A) ]
];

// recursively list all quads up to level n

// listed ccz starting with bottom slice and going up

// top and bottom faces
top = [ for(i=[0:len(B)-1]) i+len(A)+(len(A))*(steps-1) ];
bottom = [ for(i=[0:len(A)-1]) (len(A)-1)-i ];

// all faces

/// DEFINE POLYHEDRON //////////////////////////////////////////

polyhedron(
points = allpoints,
faces = allfaces
);

}
```

Once the polylofter was in place, it was just a matter of defining the vertices at the top, bottom, and middle of the scutoid. A little math helped us create two identical scutoids that next together perfectly:

You can see the full code, customize the code to create your own unique scutoid shapes, and download free scutoid models for 3D printing at our Thingiverse page:

Don’t have a printer, or want something fancy? You can order solid or hollow pairs of these scutoids at affordable 50% scale from our Shapeways shop:

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