Octahedron

An octahedron is a three-dimensional geometric figure with eight faces, twelve edges, and six vertices. All of its faces are equilateral triangles, and it is one of the five Platonic solids, which are convex polyhedra with congruent faces and the same number of faces meeting at each vertex.

Properties of an Octahedron:

• Number of Faces: 8
• Number of Edges: 12
• Number of Vertices: 6
• Face Shape: Equilateral triangle
• Platonic Solid: Yes

Formulas for Calculating Octahedron Properties:

Surface Area (A) = 2 * √3 * s²

Volume (V) = (√2 / 3) * s³

Study Guide:

To understand the concept of an octahedron, it's important to grasp the following key points:

1. Identify the defining properties of an octahedron: number of faces, edges, and vertices, as well as the shape of its faces.
2. Understand the relationship between an octahedron and the Platonic solids.
3. Be able to calculate the surface area and volume of an octahedron using the provided formulas.
4. Practice identifying and visualizing octahedra in real-world objects and situations.

By mastering these concepts and calculations, you can develop a solid understanding of octahedra and their properties.