vertex

IPA/ˈvɜːteks/
KK[vˈɚtˌɛks]IPA/ˈvɜːrteks/

vertex — noun

  • vertexsingular
  • vertexesplural

1. In geometry, the place where two straight edges meet at a corner; for shapes wit

1.nounB2
Definition

In geometry, the place where two straight edges meet at a corner; for shapes with a base, it is the tip located across from the bottom side.

Example

Each corner of a triangle is called a vertex in geometry class.

The two sides of the angle meet at a single vertex.

at + the + vertex + of + noun phrase

Common collocations
  • adjacent vertices
  • opposite vertex
  • common vertex
  • vertex of a triangle / pyramid / polygon / cube / angle
  • share a vertex
  • label a vertex
Synonyms
  • corner

    everyday word; less formal than 'vertex'; used for rooms, boxes, streets, not for abstract geometric points

  • apex

    specifically the highest vertex opposite the base; overlaps only for triangles, pyramids, and cones

  • intersection

    where lines cross each other, not just meet; reserved for crossing rather than corner-forming junctions

Grammar Patterns

vertex + of + noun phrase

at + the + vertex + of + noun phrase

plural form: vertices

Usage Note

The standard plural form in mathematics is 'vertices', though 'vertexes' is also accepted. This is the only sense that takes a plural count reading — you can refer to 'the vertices of a polygon' but not 'the vertices of a mountain'.

Common Mistakes

The vertex of a circle is at its centre.
A circle has no vertex because it has no straight edges or corners.
A vertex is defined only where straight lines meet, and a circle has no straight edges.
Each corner of the room is a vertex.
Each corner of the room can be thought of as a vertex.
In everyday contexts, 'corner' is preferred; 'vertex' is used in formal geometry contexts.

2. The highest or topmost point of a physical object, such as a mountain, arch, dom

2.nounC1
Definition

The highest or topmost point of a physical object, such as a mountain, arch, dome, or ridge.

Example

The vertex of the arch stood fifteen metres above the road.

vertex + of + physical object

Kabir took a photo from the vertex of the hill at sunrise.

Common collocations
  • vertex of a mountain / arch / dome / ridge / hill / roof
  • at the vertex
  • reach the vertex
  • near the vertex
Synonyms
  • summit

    more common for mountains; suggests a successful climb or achievement

  • apex

    interchangeable with 'vertex' in this sense; 'apex' is slightly more common for arches and curves

  • peak

    most common everyday word; used for mountains, roofs, and performance (reaching a peak)

Antonyms
  • base

    the lowest supporting part of an object

  • bottom

    the lowest point of something

Grammar Patterns

vertex + of + noun phrase

at + the + vertex + of + noun phrase

Usage Note

More formal than 'top' or 'summit'. Preferred in descriptions of architecture, sculpture, or landscape. Unlike sense 1, this sense is almost always singular and is never used in the plural to describe multiple objects.

Word family

  • vertices
    nounB2

Synonym discussion

Sense: noun/1

In geometry, 'vertex' is the precise term for the point where two straight lines meet to form an angle. 'Corner' is the everyday alternative — you would call a table's edge a 'corner', not a 'vertex', unless you were in a geometry lesson. 'Apex' overlaps only for triangles and pyramids, where it refers specifically to the vertex opposite the base (the topmost point). 'Intersection' differs in kind: it describes where two lines cross each other (as in a crossroads), not where they meet to form a corner. A vertex is always an intersection of a particular kind, but an intersection is not always a vertex. For example, the crossing point of the letter X is an intersection but not a vertex, because no angle is formed.

corner ↗apex ↗intersection ↗

Common collocations

Nouns

Phrases

  • at the vertex
  • vertex of
  • share a vertex

Prepositions

Etymology

LatinEnglish

From Latin 'vertex' (whirlpool, top of the head, summit), from 'vertere' (to turn). The original meaning was 'the top of the head' — the place where the hair forms a whorl or 'turns' — which then extended to mean 'the highest point' of anything. The mathematical use for 'corner point of a geometric figure' appeared in English in the late 1500s.