![]() ![]() Do the same to a cube, and the result is an octahedron.Ī tetrahedron can be formed by connecting centers of certain faces of the octahedron. Connect the centers of adjacent faces, and the result is a cube. Each has a unit square for a base and a height equal to the circumradius. Next, find the apothem of an equilateral triangle, and use it to find the inradius and circumradius of the octahedron.Īnother way with the volume is to dissect the octahedron into two pyramids. ![]() The dihedral angle between the two triangles is the dihedral angle of the octahedron. At each of the base vertices there are three faces, including two triangles and a square. The result is a pyramid with a square base. Four faces that meet at a common vertex are cut away from the rest of the solid. It applies only to cases in which exactly three faces meet at a vertex. There is a problem with the dihedral angle formula being use in these pages. Multiply that by the number of faces for the total surface area. The octahedron might also be classified as a square dipyramid or a triangular antiprism.Ĭonsider an octahedron with side length s. The octahedron has 8 equilateral triangular faces, 6 vertices, and 12 edges. ![]()
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