Scutoids are a geometrical solution to three-dimensional packing of epithelia as published in Nature announces the discovery of a "new" shape.
I found the mathematical definition of a scutoid to be a bit vague. I suspect that rather than being previously undiscovered, as headlines suggest, it was left unnamed because it is messy geometrically. Its closest relative the prismatoid has nice planer faces while the scutoid most often has non-planer faces and a "mid-level vertex". Subjectively speaking: the scutoid looks a bit clumsy in isolation but shines when coupled with other mating scutoids.
The importance of the shape comes from its newly discovered abundance in nature, its hidden vertex being shielded from view by adjoining cells. The paper didn't offer any euclidean definition and even left the definition vague enough to tantalize the possibility of multiple mid-level vertices and therefore hexagonal to trapezoidal transformations. The paper did; however, have helpful visuals and kernels of plain-speak explanation which I used to create the model. I focused on the tubular model with its basal and apical surfaces.
I did NOT use Voronoi calculations to create the model. This is definitely a short cut since the shape of scutoids in nature are dependant upon their Voronoi relations to neighboring cells. In fact, the realization that Voronoi cells when squeezed to a smaller surface can change both shape and configuration was the impetus for the discover. Notice how the touching red and green hexagons transform into non-touching pentagons. Likewise, the non-touching blue and yellow pentagons transform into touching hexagons.
Does this model tessellate beyond four parts?
No. I think the door is open for further exploration into how scutoids can tessellate. The paper only sites that scutoids occur in nature, not how they can be packed in a theoretical and virtual environment.
As for printing:
I've attached the original curved cell files depicting basal and apical surfaces (scutoid_arched_1-2). Although it is described as four cell, only two parts are uploaded. This is because the pair is radially symmetrical.
I recommend printing in vase mode (scutoid_vase_1-2). This speeds up the print, eliminates the need for supports, and allows one to see within the cells. For this I've attached the four cell configuration with the top and bottom chopped at parallel planes. Again, only two parts are uploaded because they are radially symmetrical.
Much thanks to previous contributors especially mathgrrl