vertices

A triangle has three vertices.

Definition

1. Noun (plural form of vertex):
   • In geometry: "vertices" are the points where two or more lines, edges, or rays meet to form an angle or corner of a shape (e.g., a polygon, polyhedron, or graph).

     • Example: A triangle has three vertices.
   • In anatomy: "vertices" refer to the topmost point of the head or skull.

     • Example: The human skull has a single vertex, but its plural "vertices" is rarely used in this sense.
   • In astronomy: "vertices" can mean the zenith point directly overhead in the sky.

     • Example: The celestial sphere has a vertex at the observer's zenith.
   • In figurative or abstract use: "vertices" can denote the highest point or peak of something, such as an argument or a curve.

     • Example: The graph of a parabola has two symmetric vertices.

Usage Examples

• Geometry:

  • A cube has eight vertices, each where three edges meet. (The corners of the cube.)
  • The polygon's vertices are labelled A, B, C, and D. (The points forming the corners of the shape.)

• Anatomy:

  • The doctor examined the vertices of the patient's skull. (The topmost parts of the head.)

• Astronomy:

  • The star appeared directly at the vertices of the observer's sky. (The zenith point.)

• Figurative:

  • The debate reached its vertices of intensity. (The highest points of argument.)

Advanced Usage

• "graph vertices": in mathematics and computer science, "vertices" are the fundamental units of a graph (also called nodes), connected by edges.

  • The graph has five vertices and seven edges. (The graph contains five points and seven connections.)

• "vertices of a polygon": the corner points defining the shape.

  • To calculate the area, list the vertices in order. (List the corner points sequentially.)

Variants and Related Words

• Vertex (singular noun): the singular form of "vertices".

  • The vertex of the triangle is at the origin. (The single corner point.)

• Vertex (as a verb form is rare): no common verb form exists.

Synonyms

• Corners: points where edges meet (in geometry).
• Apexes: the highest points (often in anatomy or figurative use).
• Nodes: intersection points in graphs or networks.
• Peaks: topmost points (in astronomy or figurative contexts).

Idioms and Phrasal Verbs

• No common idioms or phrasal verbs exist for "vertices" as it is a technical term.

Related Terms

• Edges: the lines connecting vertices in a shape or graph.
• Faces: the flat surfaces bounded by edges and vertices in a polyhedron.
• Polyhedron: a solid shape with flat faces, straight edges, and vertices.