A New Type of Polyhedron: The Scutoid

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A prism is the volume generated by translating a polygon out of its plane. The faces of consist of and its final translate and the parallelograms between the corresponding sides of and . If the translate is perpendicular to the plane of , is called a right prism.

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One way to generalize a right prism is to shrink one or more of the sides of the polygons or to a point. This is called a prismatoid. In this Demonstration, the original polygon is a hexagon and one of the sides of the base is shrunk to a point so that the base becomes a pentagon.

A scutoid is a recently defined [1, 2] modification of such a prismatoid in which the two converging edges are replaced by a Y-shaped intersection.

Scutoids were first identified and named by P. Gómez-Gálvez and coworkers in their study of the three-dimensional packing of epithelial cells [3]. Networks of scutoids are suggested as possible structures for biological membranes since they can maintain curved yet rigid configurations.

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Contributed by: S. M. Blinder  (September 2018)
Open content licensed under CC BY-NC-SA


Details

References

[1] A. Burdick, "We Are All Scutoids: A Brand-New Shape, Explained." The New Yorker. (July 30, 2018) www.newyorker.com/elements/lab-notes/we-are-all-scutoids-a-brand-new-shape-explained.

[2] Wikipedia. "Scutoid." (Aug 29, 2018) en.wikipedia.org/wiki/Scutoid.

[3] P. Gómez-Gálvez, P. Vicente-Munuera, A. Tagua, C. Forja, A. M. Castro, M. Letrán, A. Valencia-Expósito, et al., "Scutoids Are a Geometrical Solution to Three-Dimensional Packing of Epithelia," Nature Communications, 9(1), 2018 pp. 1–14. doi:10.1038/s41467-018-05376-1.


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