regular tetrahedron

Thân thiện

A student constructs a regular tetrahedron from paper.

Definition

Noun: A regular tetrahedron is a specific type of three-dimensional geometric solid (a polyhedron) composed of four faces. All four faces are congruent equilateral triangles, and all edges are of equal length. It is one of the five Platonic solids.

Usage

The term is used in geometry, mathematics, engineering, and crystallography to describe a perfectly symmetrical tetrahedron. * In geometry, a regular tetrahedron is the simplest Platonic solid. * The methane molecule (CH₄) has a shape that approximates a regular tetrahedron. * To calculate the volume, you need the length of an edge of the regular tetrahedron.

Advanced Usage

• In coordinate geometry: A regular tetrahedron can be conveniently defined with vertices at specific coordinates, such as (1, 1, 1), (1, -1, -1), (-1, 1, -1), and (-1, -1, 1).
• Dual polyhedron: The regular tetrahedron is self-dual, meaning its dual polyhedron is another regular tetrahedron.

Variants and Related Words

• Tetrahedron (n): A more general polyhedron with four triangular faces, which are not necessarily equilateral or congruent.
• Platonic solid (n): Any of the five convex regular polyhedra (tetrahedron, cube, octahedron, dodecahedron, icosahedron).

Synonyms

• Equilateral tetrahedron (less common but descriptive)

Antonyms

• Irregular tetrahedron (a tetrahedron with faces that are not all congruent equilateral triangles)

Học thuật

Noun

1. a tetrahedron with four equilateral triangular faces