In reality, probably nothing since the universe itself may be finite. However, in abstract or conceptual terms, most 3-d objects can have infinite versions.
You may have in mind the common sphere. Because of one interesting property of spheres they are sometimes used as an analogy for some models that suggest the universe is 'finite and unbounded'. This might be what you are thinking of that is related to but not identical with the infinite. The surface of a sphere, like the earth's surface, is finite (there is only so much area and no more), yet it is unbounded. You can travel in a given direction and you will never come to a point where you have to leave earth's surface. You may arrive at your starting point again if you travel in what is the best estimate of a 'straight line', or you might even wander for extremely long periods of time, crossing paths you have been on before, and you would never be required to actually return to your starting point. This analogy serves to demonstrate the idea of 'finite and unbounded', and applying the concept to space involves models much more complex and subtle than a simple sphere.
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That's more of a statement than a question. It's also a false statement. You can build a three dimensional object from two dimensional objects, if you have an infinite number of them.
A plane
Area is a two-dimensional measurement. It tells you how big a two dimensional object is or how large the surface of a three-dimensional object is.Volume is a three dimensional measurement. It tells you how big the inside of a three-dimensional object is or how much a three-dimensional object can hold inside.
All three dimensional figures have more faces than a one dimensional figure. There are an infinite number of one dimensional points on a three dimensional figure
infinite width, contains a plane and is three dimensional