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Diamond Or cone * * * * * Partly correct. A rhombus can be called a diamond or a parallelogram or a quadrilateral. However, a rhombus is a 2-dimensional figure whereas a cone is 3-dimensional so you certainly could not call a rhombus a cone.
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3-dimensional
The net of a 2 dimensional shape can be folded into a 3 dimensional shape
A hexagon is a 2-dimensional shape. A "structure" implies a 3-dimensional shape but you have not specified whether it is a hexagonal pyramid, a hexagonal prism or some other shape that is [partly] based on a hexagon. Without that information it is not possible to give a more helpful answer.