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.
An octahedron is a type of polyhedron, specifically a solid, that has eight triangular faces. It is not classified as a pyramid or a prism; instead, it can be considered a type of convex solid. The octahedron has 6 vertices and 12 edges, distinguishing it from the characteristics of pyramids and prisms.
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.
To construct an octahedron using square pyramids, you need a total of 8 square pyramids. Each pyramid can be placed with its base facing outward, sharing a vertex at the center of the octahedron. This arrangement allows the pyramids to form the eight triangular faces of the octahedron.
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.
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.
A regular octahedron and a heptagonal pyramid.A regular octahedron and a heptagonal pyramid.A regular octahedron and a heptagonal pyramid.A regular octahedron and a heptagonal pyramid.
No, it is not.
Not necessarily. A heptagon-based pyramid is an octahedron and it has no parallel faces.
An octahedron is a type of polyhedron, specifically a solid, that has eight triangular faces. It is not classified as a pyramid or a prism; instead, it can be considered a type of convex solid. The octahedron has 6 vertices and 12 edges, distinguishing it from the characteristics of pyramids and prisms.
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.
Here are three; cube, octahedron, hexagonal pyramid.
An octahedron
To construct an octahedron using square pyramids, you need a total of 8 square pyramids. Each pyramid can be placed with its base facing outward, sharing a vertex at the center of the octahedron. This arrangement allows the pyramids to form the eight triangular faces of the octahedron.
The platonic solids are: a tetrahedron, a cube, an octahedron, dodecahedron and icosahedron. A pyramid has a base with triangles attached to it with a common vertex. The platonic solid that is a pyramid is a tetrahedron (a triangular based pyramid).
An octahedron is the name for a non-specific shape. It could, as described above, be a di-rectangular pyramid with 6 vertices. 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.
You start with a quadrilateral based bipyramid, which has six vertices. At each vertex, remove the tip in the form of a quadrilateral based pyramid. You will be left with a truncated octahedron.
A tetrahedron, a triangle based pyramid, an octahedron, an icosahedron plus many more.