Definition

1. Noun:
   • A polyhedron with eight plane faces: An octahedron is a three-dimensional geometric solid that has exactly eight flat polygonal faces. It is one of the five Platonic solids, where each face is an equilateral triangle and the shape is highly symmetrical.

Examples of Usage

• Noun:
  • The crystal had a perfect octahedron shape.
  • In geometry class, we constructed a model of an octahedron from paper.
  • A regular octahedron has eight faces that are all congruent equilateral triangles.

Advanced Usage

• "Regular octahedron": The most common and symmetrical form, where all eight faces are identical equilateral triangles.
  • The diamond crystal was a nearly perfect regular octahedron.
• "Truncated octahedron": An Archimedean solid formed by cutting off the corners of a regular octahedron, resulting in a shape with 14 faces (6 squares and 8 regular hexagons).
  • Some molecular structures are modeled as truncated octahedra.

Variants and Related Words

• Octahedral (adj): Having the form of an octahedron; relating to an octahedron.
  • The molecule has an octahedral geometry.
• Octahedrite (n): A mineral, a variety of anatase (titanium dioxide), which commonly occurs in octahedral crystals.

Synonyms

• Eight-faced polyhedron: A descriptive synonym.
• Platonic solid (when regular): A broader category that includes the octahedron.

Related Phrases and Terms

• Dual polyhedron: For a regular octahedron, the dual polyhedron is a cube (connecting the centers of the octahedron's faces creates a cube).
  • The cube and the octahedron are dual polyhedra.
• Face, Edge, Vertex: The octahedron has 8 faces, 12 edges, and 6 vertices.

Noun

1. any polyhedron having eight plane faces