An octahedron is a room number with 8 faces that are polygons. In the number below are 3 different forms of octahedrons. The presolve "octa" means eight.

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An octahedron have the right to be formed by two pyramids via bases in the shape of a quadrilateral, as shown in the number listed below.

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Properties of a continuous octahedron

A constant octahedron is an octahedron whose faces are all congruent, constant polygons. Otherwise, it is irconsistent. Regular octahedrons are studied even more frequently.

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A continuous octahedron, such as the one shown over, is one of the 5 Platonic solids, which are a form of continuous polyhedron. A consistent octahedron has 8 congruent deals with that are congruent equilateral triangles, 12 congruent edges, and also 6 vertices; an edge is a line segment developed by the intersection of 2 surrounding faces; a vertex for a continuous octahedron is a suggest wbelow 4 edges fulfill.

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Surconfront area of a regular octahedron

We can uncover the location of one of the encounters and multiply it by eight to discover the total surface location of a regular octahedron. An equilateral triangle with side length, e (likewise the length of the edges of a consistent octahedron), has actually a room, A, of

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The full surconfront area, S, of a continuous octahedron in regards to its edges, e, is,

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Volume of a continual octahedron

The volume, V, of a consistent octahedron is

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wright here e is the length of the edge.


Example:

If the total surconfront area of a consistent octahedron is

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, what is its volume?

We have the right to discover e by substituting the provided worth in for the complete surchallenge area to get