How does a tiling of the hyperbolic plane look on the hyperboloid model?

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How does a tiling of the hyperbolic plane look on the hyperboloid model?

For example this tiling:

enter image description here

My understanding is this is how a hyperboloid looks like if viewed from the origin, or something like that. is there a tool where one can view (a truncated) hyperboloid surface that is tiled. For example, would the tiles on the sides still look circular if viewed from a normal angle? I am assuming not, but i wouldnt have assumed a conical slice to be elliptical either.