A scutoid is a particular type of geometric solid between two parallel surfaces. The boundary of each of the surfaces (and of all the other parallel surfaces between them) either is a

polygon In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed '' polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two ...

or resembles a polygon, but is not necessarily planar, and the vertices of the two end polygons are joined by either a curve or a Y-shaped connection on at least one of the edges, but not necessarily all of the edges. Scutoids present at least one

vertex Vertex, vertices or vertexes may refer to: Science and technology Mathematics and computer science *Vertex (geometry), a point where two or more curves, lines, or edges meet *Vertex (computer graphics), a data structure that describes the position ...

between these two planes. Scutoids are not necessarily convex, and lateral faces are not necessarily planar, so several scutoids can pack together to fill all the space between the two parallel surfaces. They may be more generally described as a mix between a frustum and a

prismatoid In geometry, a prismatoid is a polyhedron whose vertices all lie in two parallel planes. Its lateral faces can be trapezoids or triangles. If both planes have the same number of vertices, and the lateral faces are either parallelograms or ...

Naming

The object was first described by Gómez-Gálvez ''et al.'' in a paper entitled ''Scutoids are a geometrical solution to three-dimensional packing of epithelia'', and published in July 2018. Officially, the name ''scutoid'' was coined because of its resemblance to the shape of the

scutum The ''scutum'' (; plural ''scuta'') was a type of shield used among Italic peoples in antiquity, most notably by the army of ancient Rome starting about the fourth century BC. The Romans adopted it when they switched from the military formatio ...

and scutellum in some insects, such as beetles in the subfamily Cetoniinae. Unofficially, Clara Grima has stated that while working on the project, the shape was temporarily called an ''Escu''-toid as a joke after the biology group leader Luis M. Escudero. Since his last name, " Escudero", means "squire" (from Latin ''scutarius'' = shield-bearer), the temporary name was modified slightly to become "scutoid".

Appearance in nature

Epithelial Epithelium or epithelial tissue is one of the four basic types of animal tissue, along with connective tissue, muscle tissue and nervous tissue. It is a thin, continuous, protective layer of compactly packed cells with a little intercellu ...

cells adopt the "scutoidal shape" under certain circumstances. In epithelia, cells can 3D-pack as scutoids, facilitating tissue curvature. This is fundamental to the shaping of the organs during development.

"Scutoid is a
prismatoid In geometry, a prismatoid is a polyhedron whose vertices all lie in two parallel planes. Its lateral faces can be trapezoids or triangles. If both planes have the same number of vertices, and the lateral faces are either parallelograms or ...
to which one extra mid-level vertex has been added. This extra vertex forces some of the " faces" of the resulting object to curve. This means that Scutoids are not
polyhedra In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on ...
, because not all of their faces are planar. ... For the computational biologists who created/discovered the Scutoid, the key property of the shape is that it can combine with itself and other geometric objects like frustums to create 3D packings of epithelial cells."
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Laura Taalman Laura Anne Taalman, also known as mathgrrl, is an American mathematician known for her work on the mathematics of Sudoku and for her mathematical 3D printing models. Her mathematical research concerns knot theory and singular algebraic geometry; ...

Cells in the developing lung epithelium have been found to have more complex shapes than the term "scutoid", inspired by the simple scutellum of beetles, suggests. When "scutoids" exhibit multiple Y-shaped connections or vertices along their axis, they have therefore been called "punakoids" instead, as their shape is more reminiscent of the

Pancake Rocks A pancake (or hotcake, griddlecake, or flapjack) is a flat cake, often thin and round, prepared from a starch-based batter that may contain eggs, milk and butter and cooked on a hot surface such as a griddle or frying pan, often frying wit ...

Punakaiki Punakaiki is a small village on the West Coast of the South Island of New Zealand. It is located between Westport and Greymouth on , the only through-road on the West Coast. Punakaiki is immediately adjacent to Paparoa National Park, and is al ...

New Zealand New Zealand ( mi, Aotearoa ) is an island country in the southwestern Pacific Ocean. It consists of two main landmasses—the North Island () and the South Island ()—and over 700 smaller islands. It is the sixth-largest island coun ...

Potential uses

The scutoid explains how

epithelial cells Epithelium or epithelial tissue is one of the four basic types of animal tissue, along with connective tissue, muscle tissue and nervous tissue. It is a thin, continuous, protective layer of compactly packed cells with a little intercellu ...

(the cells that line and protect organs such as the skin) efficiently pack in three dimensions. As epithelial tissue bends or grows, the cells have to take on new shapes to pack together using the least amount of energy possible, and until the scutoid's discovery, it was assumed that epithelial cells packed in mostly frustums, as well as other prism-like shapes. Now, with the knowledge of how epithelial cells pack, it opens up many new possibilities in terms of artificial organs. The scutoid may be applied to making better artificial organs, allowing for things like effective organ replacements, recognizing if a person's cells are packing correctly or not, and ways to fix that problem.

References

External links

THE SCUTOID: did scientists discover a new shape?
- Matt Parker at Youtube {{Use dmy dates, date=April 2019 Volume Zonohedra Epithelium