How do you imagine an infinite object which has 3 dimensional extension.
I think I can elaborate on this a bit.
I can imagine a space with elliptical geometry. I can also imagine a space with Euclidean geometry. The defining difference between these two geometries is the number of lines in a plane parallel to a given line you can draw through a point. That's a fairly complex concept, but I get it. In elliptical geometries, you cannot draw such a line. In Euclidean geometries, you can.
Considering such parallel lines in a plane, in a Euclidean geometry, I can imagine that they would never touch. I find it very easy to imagine this--I don't know exactly why I find it so easy, but the symmetry is simple to imagine. No matter where I go along the line, it looks the same. The lines aren't closer together anywhere, so they never touch.
In the same Euclidean geometry, I can imagine the two Euclidean solids formed by the set of all points less than a certain distance from either line--forming a cylindrical rod shape. Just as easily, to me, as I can imagine that the lines never touching in a Euclidean geometry, I can imagine these solids never touching.
Imbue the solids with mass, and I have a simple qualitative common model of rods in the universe. I know this isn't physically accurate, but that's okay--I can go further by imagining that they are made of iron molecules. If need be I can imagine that they are 20 degrees centigrade, very slightly rusted, and/or anything that might come into relevance for particular problems. But I cannot think of anything that would preclude me from imagining it. The "actuality" attribute to you seems to be a problem--to me it seems completely irrelevant. I measure actuality based on whether or not I find something, not whether or not I can imagine it; the act of imagining "an actual rod" to me seems to be the same exact act as imagining a rod, with the trivial addition that I ran into one.
All I'm doing here, all throughout, is applying symmetries. Beyond this I don't know what to explain. I can just say that I can imagine such a rod.