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If the pyramid has a triangular sides then truncate each vertex (cut off a small pyramid shape from the vertices).
If the pyramid has a quadrilateral base then truncate 3 vertices.
If the pyramid has a pentagonal base then truncate 2 vertices.
If the pyramid has a hexagonal base then truncate 1 vertex.
If the pyramid has a heptagonal base then it is already an octahedron.
If the pyramid has an base with 8 or more vertices then slice off the section formed by joining the apex and two vertices from the base which are six apart. This makes the base heptagonal and therefore the shape is an octahedron.
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Why is a truncated octahedron called a truncated octahedron?
Start with an octahedron in the form of a quadrilateral based dipyramid a regular octahedron is a special case of this). This shape has six vertices - chop these off so as to remove a quadrilateral based pyramid. You will be left with a truncated octahedron. It is an octahedron which has been truncated (shortened) by cutting off its extremities.
Is a octahedron a pyramid?
It can be but need not be. A heptagon-based pyramid is an octahedron. However, the term is often used for the Platonic solid bounded by eight equilateral triangles - in the form of two square based pyramids stuck together base-to-base.
How do you find the volume of a octahedron pyramid?
The general formula for any type of pyramid - as well as for cones - is (1/3)Bh, where "B" is the base area, and "h" is the perpendicular height.
How many vertices does octahedron have have?
An octahedron is the name for a non-specific shape. It could be a di-rectangular pyramid with 6 vertices - this is like two rectangular [or square] based pyramids stuck together base-to-base. Or it could be a heptagonal pyramid, in which case it has 8 vertices. Or it could be a hexagonal prism, in which case it has 12 vertices. There are other octahedraons.
What has all the faces the same has equilateral triangles has eight faces and is a polyhedrom?
Octahedron. It is two square pyramids that share a base (Imagine a pyramid from Egypt, flip it upside down, and stick that to the bottom of the original pyramid).
