A rhombus is a two dimensional object, a rhomboid is 3 dimensional. The relation between the two is the same as that between a square and a cube.
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The adjective for a rhombus or rhomboid is rhombic.
rhomboid or parallelepiped
A rectangle, square, rhombus, and rhomboid are all parallelograms.
Diamond is another name for rhombus.
the shape