Scutoid

thingiverse

The scutoid has hit the news as a 'new' shape discovered in the structure of the epithelia. See the article in Nature https://www.nature.com/articles/s41467-018-05376-1 Previously the cells were assumed to be prisms or frustrums where the upper and lower faces have the same number of edges, but the scutoid has different numbers of edges (here 5 and 6), the difference being made up by a triangular face with a vertex lying between the upper and lower faces. Ed Pegg https://math.stackexchange.com/questions/2864794/the-scutoid-a-new-shape derived a form of the scutoid with planar surfaces. I have re-oriented his version and elongated it in the vertical direction to make it look more like the shapes in the paper. The openscad code is included here but it is better to generate your own version from my polyhedral index where alternative forms can be selected http://kitwallace.co.uk/3d/solid-index.xq?mode=solid&id=scutoid-O The scutoid of the article has non-planar surfaces.. The last vertex is the mid-layer apex of the triangular face, so moving this point forces the adjacent faces to twist and become non-planar. It would of course be preferable to generate random scutoids - a project for another day.