A New Type of Polyhedron: The Scutoid

prism to prismatoid

prismatoid to scutoid

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.

One way to generalize a right prism is to shrink one or more of the sides of the polygons

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.

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.

Permanent Citation

S. M. Blinder

"A New Type of Polyhedron: The Scutoid"
http://demonstrations.wolfram.com/ANewTypeOfPolyhedronTheScutoid/
Wolfram Demonstrations Project
Published: September 14, 2018