Definition

1. Noun:
   • A regular icosahedron is a specific three-dimensional geometric shape. It is a type of polyhedron that has exactly twenty faces. All of these faces are identical equilateral triangles. It is one of the five Platonic solids, meaning it is a convex, regular polyhedron.

Usage

• The term "regular icosahedron" is used in geometry, mathematics, crystallography, and fields involving three-dimensional design or modeling. It describes a perfectly symmetrical shape with specific properties.
• It is typically used as a countable noun (e.g., , ).

Examples

• Noun:
  • In geometry class, we constructed a model of a regular icosahedron using paper and glue.
  • The virus's capsid has the shape of a regular icosahedron.
  • Of the five Platonic solids, the regular icosahedron has the greatest number of faces.

Advanced Usage

• "Regular icosahedral symmetry": Refers to the high degree of symmetry (icosahedral symmetry group) exhibited by the shape, often discussed in advanced mathematics and theoretical physics.
  • The molecule's structure exhibits regular icosahedral symmetry.

Variants and Related Words

• Icosahedron (n): A more general term for any polyhedron with twenty faces. The faces may not be equilateral or identical. A icosahedron is a specific type of icosahedron.
• Icosahedral (adj): Having the form of an icosahedron.
  • The viral capsid has an icosahedral structure.
• Platonic solid (n): Any of the five regular, convex polyhedra (tetrahedron, cube, octahedron, dodecahedron, icosahedron).

Synonyms

• Regular twenty-faced polyhedron: A descriptive synonym.
• One of the Platonic solids: A categorical synonym placing it within a known group.

Related Terms and Concepts

• Dual polyhedron: The dual polyhedron of a regular icosahedron is the regular dodecahedron.
• Schläfli symbol: The Schläfli symbol for the regular icosahedron is {3,5}, indicating that five equilateral triangles (3-sided figures) meet at each vertex.

Noun

1. an icosahedron with twenty equilateral triangles as faces