A quick google search turns up many images of $2D$ Penrose diagrams but no $3D$ ones.
Q: What does a $3D$ Penrose diagram look like?
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In a Carter-Penrose diagram spacetime is asumed to be spherically symmetrical, so up to symmetry only one space coordinate is needed. Adding a second space axis would then not capture or reveal any new information. If you want to add something other than a space axis, then how it would look like depends on what is it that you are adjoining. – Randy Marsh Nov 21 '19 at 23:28
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Can I add an entropy axis? – John Zimmerman Nov 23 '19 at 19:29
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@RandyMarsh are penrose diagrams causal diamonds? – John Zimmerman Feb 26 '22 at 19:13