# equilateral

equi·​lat·​er·​al | \ ˌē-kwə-ˈla-tə-rəl , ˌe-, -ˈla-trəl \

## Definition of equilateral

1 : having all sides equal an equilateral triangle an equilateral polygon
2 : having all the faces equal an equilateral polyhedron

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## Did You Know?

Since equi- means "equal", the meaning of equilateral is easy to guess from its roots. The word is mostly used in geometry. The standard polygons (many-sided geometrical shapes)—the pentagon, hexagon, octagon, etc.—are assumed to be equilateral if we don't say otherwise; an equilateral rectangle has the special name square. But triangles are particularly important, and many triangles are not equal-sided. The standard polyhedrons (many-sided solids) are also equilateral. Most common is the cube, all of whose sides are square. The tetrahedron has four triangular sides and thus is a pyramid with a triangular base, unlike the pyramids of Egypt with their square bases.

## Examples of equilateral in a Sentence

Recent Examples on the Web The group can be expressed as a set of mathematical matrices — arrays of numbers that, when multiplied by coordinates of an equilateral triangle, return the same coordinates. One popular design is based on the mathematical structure of an icosahedron, a three-dimensional shape built from equilateral triangles. For the four Platonic solids built out of squares or equilateral triangles — the cube, tetrahedron, octahedron and icosahedron — mathematicians recently figured out that the answer is no. Squares, hexagons and equilateral triangles can do it. Plato turned that into the Platonic solids, which are a series of regular 3D shapes, meaning with sides that are all squares, for example, or equilateral triangles—the 3D versions of different regular 2D polygons. That’s when an equilateral triangle becomes an isosceles, often with one person isolated at the farthest point. That’s when an equilateral triangle becomes an isosceles, often with one person isolated at the farthest point. But most groups are far more difficult to understand than the symmetry group of an equilateral triangle.

These example sentences are selected automatically from various online news sources to reflect current usage of the word 'equilateral.' Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

## First Known Use of equilateral

1570, in the meaning defined at sense 1

## History and Etymology for equilateral

Late Latin aequilateralis, from Latin aequi- + later-, latus side — more at lateral

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Time Traveler for equilateral ## The first known use of equilateral was in 1570

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## Dictionary Entries near equilateral

equilateral hyperbola

## Statistics for equilateral

Last Updated

19 Dec 2020

Cite this Entry

“Equilateral.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/equilateral. Accessed 28 Jan. 2021.

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More Definitions for equilateral

equilateral

equi·​lat·​er·​al | \ ˌē-kwə-ˈla-tə-rəl , ˌe-kwə- \

## Kids Definition of equilateral

: having all sides or faces equal an equilateral triangle

More from Merriam-Webster on equilateral

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