Solid geometry.
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The question is not clear. Hardest, as in the most rigid, is a triangular prism (or tetrahedron). Hardest, to work the geometry of, is probably an irregular blob.
* geometry in nature * for practcal use of geometry * geometry as a theory * historic practical use of geometry
Oh, dude, the largest 3D shape is technically the infinite plane, because it goes on forever in all directions. But if you're looking for a more tangible answer, the sphere takes the crown as the largest 3D shape in terms of volume. So, like, if you're ever lost in a geometry maze, just remember, spheres are the big boys of the 3D world.
A vertex is defined in Geometry and the point at which two lines or segments connect. If we think of a 2D square first we can count that it in fact has 4 vertices. One at the top left, one at the top right, one at the bottom left, and one at the bottom right. We understand in Geometry that a 3D object is a 2D object with an additional plane of space. So knowing this we can assume that there would have to be an additional 4 vertices to formulate a 3 Dimensional square - which is now a cube. So in conclusion If a 2D object has 4 vertices, then a 3D object since it has an additional plane of space would need an additional 4 vertices to make a square on the second plane of space. So we need a total of 8 vertices to make a 3D cube (3D square - though in technicality a square is 2D, a cube is 3D)
3 dimensional geometry.3 dimensional geometry.3 dimensional geometry.3 dimensional geometry.