Yes,
check your average calculus book after you get past differentiation and integration for instructions. (It won't make sense cause as humans we've only got three of them) Figure always describes a phenomenon. There may be two, three or more definitive units. You may use figures for simple processes like "income per month through year" or for complicated like "iron melting with so many ingredients". Two dimensions may be drawn on paper sheet. Three dimensions are usually made by copying two dimension figures with a very small spaces. Four and more dimensions are easy to perform on computer screen. Some atempts are often made in drawing 4D on paper sheet but results are not very understandable. It is important not to be afraid of more dimensions. An understandable example is proofing dough. What units should be in the figure: Time, Temperature, Mass, Volume, Condition of Yeast, Percentage of Salt etc. Every cook can cope with such a six dimensional figure even without drawing. If we use the common ideas for dimensions, then even a 3D figure cannot be drawn on a 2D surface (paper) because it can only be one view of the 3D surface not all views at the same time. 4D would be even more of a challenge when you think of a normal 3D object being just one view of a 4D object. Salvador Dali was very interested in this question and particularly being able to represent higher dimensional objects (at least some limited view of one) in some of his work. There is a famous work, Crucifixion (Corpus Hypercubus), which shows Christ crucified on a hypercube (that is a cube in 4D space). I think generally that such a representation is of limited usefulness as a static object on paper and that an animated object is more representative (see the WIKI page for hypercube). Some people think of time as the 4th dimension, in which case you could represent the changes in 3D objects over time (as in a cartoon animation). In reality, however, a third dimension (depth) is only an optical illusion when represented on a 2D surface (paper) and a matter of the perception of the viewer (see visual illusions).
If it is a 2-dimensional figure then it is a quadrilateral. If it is a 3-dimensional figure then it is a tetrahedron.
A pyramid is a four-sided, three-dimensional figure.
A hypercube is a four dimensional figure.
A three dimensional figure with polygonal faces is called a polyhedron. Specific names draw from the Latin prefixes. For example a four sided figure is a tetrahedron.
tetrahedron
square
A quadrilateral.
Yes, of course. Higher dimensions as well. But since the space we live in happens to have only 3 dimensions, it is difficult to draw, or imagine, such figures.
rhombus
a 2 dimensional figure with four sides and all four angles =90 degrees= pi/2 radians
A regular tetrahedron
A three dimensional triangular figure with three faces and a base is called a triangular pyramid. It has four vertices, four faces, and six edges.