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There is more than one possibility.

If by a diamond you mean a square tilted up onto a corner, and you wnt a 3D shape something like that, probably the best answer is an octahedron, which has 8 triangles as faces; see http://en.wikipedia.org/wiki/Octahedron.

You might also go for the triangular dipyramid, which has 6 triangular faces and is made by sticking two triangular pyramids together;
see http://polyhedra.org/poly/show/56/triangular_dipyramid - you can rotate the image to get a better idea of what it looks like. There are other dipyramids: the square dipyramid is the same as the octahedron; there is also a pentagonal dipyramid and more.

It is better to actually make some of these by cutting equilateral triangles out of paper and sticking them together.

If you mean what shape is a real diamond in a piece of jewellery, that is a specialised topic, which I don't know about. There are some images of different diamond cuts at
http://en.wikipedia.org/wiki/Diamond_cut.
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Q: What does a 3D diamond shape look like?
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What is a diamond like 3D shape?

A parallellopiped


Why is a diamond a 3d shape?

A cut diamond is a 3D object as it has length, width and depth (even if it is roundish like a pebble)


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A diamond is a 3D shape, specifically a type of polyhedron known as a rhombus. A rhombus is a quadrilateral with all sides of equal length, opposite sides parallel, and opposite angles equal. In a three-dimensional space, a diamond shape is a polyhedron with four faces that are congruent rhombi.


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A rhombus is a four sided polygon, a quadrilateral. It is a 2d shape. 2d shapes have 2 dimensions, like length and width. 3d shapes have 3 dimensions, like length, width and depth.


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Yes but the correct term is octohedron


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A parallelogram in 3D looks like a flat, four-sided shape where opposite sides are parallel. It can appear as a slanted rectangle or a diamond shape depending on the orientation of the sides. The angles between the sides can be acute, obtuse, or right angles.


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