Why is the octahedron called a Platonic solid?

It's one of five Platonic solids: all faces are congruent regular polygons, and the same number of faces meet at each vertex.

How many vertices, edges, and faces does an octahedron have?

The octahedron has 6 vertices, 12 edges, and 8 equilateral triangular faces.

What is the dual polyhedron of an octahedron?

The cube (hexahedron) is the dual. Its vertices correspond to the octahedron's face centers.

Mathematics

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Edge Length (a)

A regular octahedron is one of the five Platonic solids, with 8 equilateral triangular faces, 12 edges, and 6 vertices. It looks like two square pyramids joined at the base.

Symbol	Name	Unit	Description
a	edge length	length	—
V	volume	length³	—
SA	surface area	length²	—

Edge a	Volume	Surface Area
1	0.47	3.46
2	3.77	13.86
4	30.17	55.42
6	101.82	124.71

References

›Octahedron — Wolfram MathWorld

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