Regular octahedron Dimensions. If the edge length of a regular octahedron is a, the radius of a circumscribed sphere (one that touches the octahedron at all vertices) is = ≈ ⋅ and the radius of an inscribed sphere (tangent to each of the octahedron's faces) is = ≈ ⋅ while the midradius, which touches the middle of each edge, is. It is one of the five platonic solids (the other ones are tetrahedron, cube, dodecahedron and icosahedron). It has 8 faces, 12 edges and 6 vertices. The volume of.

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Octahedron Facts

Notice these interesting things:

• It has 8 Faces
• Each face is an Equilateral Triangle
• It has 12 Edges
• It has 6 Vertices (corner points)
• and at each vertex 4 edges meet
• It is one of the Platonic Solids

Volume and Surface Area

Volume = (√2)/3 × (Edge Length)³

Surface Area = 2 × √3 × (Edge Length)²

It is called an octahedron because it is a polyhedron that has 8 (octa-) faces, (like an octopus has 8 tentacles)

When we have more than one octahedron they are called octahedra

When we say 'octahedron' we often mean 'regular octahedron' (in other words all faces are the same size and shape), but it doesn't have to be - this is also an octahedron, even though all faces are not the same. (But it may be better to call it a hexagonal prism).

8-Sided Dice? Yes! An octahedron that has 8 equal faces has an equal chance of landing on any face.

In fact, you can make fair dice out of all of the Platonic Solids.