A scutoid is a particular type of

geometric solid In mathematics, solid geometry or stereometry is the traditional name for the geometry of Three-dimensional space, three-dimensional, Euclidean spaces (i.e., 3D geometry). Stereometry deals with the measurements of volumes of various solid fig ...

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 toge ...

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 In geometry, a (from the Latin for "morsel"; plural: ''frusta'' or ''frustums'') is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting this solid. In the case of a pyramid, the base faces are p ...

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 trape ...

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 formati ...

and scutellum in some insects, such as beetles in the subfamily

Cetoniinae Flower chafers are a group of scarab beetles, comprising the subfamily Cetoniinae. Many species are diurnal and visit flowers for pollen and nectar, or to browse on the petals. Some species also feed on fruit. The group is also called fruit an ...

. Unofficially,

Clara Grima Clara Isabel Grima Ruiz (born 1971) is a professor of applied mathematics at the University of Seville, specializing in computational geometry. She is known for her research on scutoids (polyhedron-like shapes that can pack the space between pairs ...

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 Escudero is a surname. Notable people with the surname include: *Abraham Escudero Montoya (1940–2009), Roman Catholic bishop of the Roman Catholic Diocese of Palmira, Colombia *Adrián Escudero (1927–2011), Spanish footballer *Al Escudero (born ...

", 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 intercellula ...

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 trape ...
to which one extra mid-level vertex has been added. This extra vertex forces some of the "
faces The face is the front of an animal's head that features the eyes, nose and mouth, and through which animals express many of their emotions. The face is crucial for human identity, and damage such as scarring or developmental deformities may affe ...
" 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 t ...
, because not all of their faces are
planar Planar is an adjective meaning "relating to a plane (geometry)". Planar may also refer to: Science and technology * Planar (computer graphics), computer graphics pixel information from several bitplanes * Planar (transmission line technologies), ...
. ... 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 a ...

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 count ...

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 intercellula ...

(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 Prism usually refers to: * Prism (optics), a transparent optical component with flat surfaces that refract light * Prism (geometry), a kind of polyhedron Prism may also refer to: Science and mathematics * Prism (geology), a type of sedimentary ...

-like shapes. Now, with the knowledge of how epithelial cells pack, it opens up many new possibilities in terms of

artificial organ An artificial organ is a human made organ device or tissue that is implanted or integrated into a human — interfacing with living tissue — to replace a natural organ, to duplicate or augment a specific function or functions so the patient m ...

s. 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?
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Matt Parker Matthew Thomas Parker (born 22 December 1980) is an Australian recreational mathematician, author, comedian, YouTube personality and science communicator based in the United Kingdom. His book ''Humble Pi'' was the first maths book in the UK to ...

at Youtube {{Use dmy dates, date=April 2019 Volume Zonohedra Epithelium