regular dodecahedron

Thân thiện

A student holds a regular dodecahedron in math class.

Definition

Noun: A regular dodecahedron is a specific three-dimensional geometric shape. It is a type of polyhedron (a solid figure with many flat faces) defined by two key properties: 1. It has exactly twelve faces. 2. Each of these twelve faces is a regular pentagon, meaning all five sides are of equal length and all five interior angles are equal. Furthermore, in a regular polyhedron, all faces are identical regular polygons, and the same number of faces meet at every vertex (corner). In a regular dodecahedron, three regular pentagons meet at each vertex.

Usage Examples

• Noun:
  • In geometry class, we constructed a model of a regular dodecahedron out of paper.
  • The soccer ball's pattern is based on a truncated regular dodecahedron.
  • Plato associated the regular dodecahedron with the element of the cosmos or ether.

Advanced Usage

• In Mathematics and Geometry: The regular dodecahedron is one of the five Platonic solids, which are the only convex regular polyhedra. It is often studied for its symmetry and unique properties.
• In Science and Nature: While not common in crystalline structures, the shape appears in some viral capsids and quasi-crystals. It is also a favored shape in architecture and design for its aesthetic symmetry.

Variants and Related Words

• Dodecahedron (noun): The general term for any polyhedron with twelve faces. The faces can be any polygon shape (e.g., rhombi, irregular pentagons). A is a specific, highly symmetric type of dodecahedron.
• Platonic Solid (noun): A category of five regular, convex polyhedra, which includes the regular dodecahedron, tetrahedron, cube, octahedron, and icosahedron.
• Pentagon (noun): A polygon with five sides. A is the two-dimensional shape that forms each face of a regular dodecahedron.

Synonyms

• Platonic Dodecahedron: A less common but technically accurate synonym, emphasizing its membership in the set of Platonic solids.

Related Concepts

• Dual Polyhedron: The regular dodecahedron and the regular icosahedron are duals of each other. This means the vertices of one correspond to the faces of the other.
• Schläfli Symbol: The regular dodecahedron is denoted by the Schläfli symbol {5,3}, indicating that its faces are pentagons ({5}) and three meet at each vertex (3).

Học thuật

Noun

1. a dodecahedron with twelve regular pentagons as faces