1 | initial version |

If by "visualize" you mean "give a geometric realization of" then I think that the answer should be "no" as I rather suspect that there are high-dimensional combinatorial polytopes that have no geometric realization. Even for three-dimensional polytopes the realization problem is involved - there are several layout algorithms for planar graphs. (There is at least one such implemented in sage - see:

http --- fix --- doc.sagemath.org/html/en/reference/plotting/sage/graphs/graph_plot.html

). On the other hand, if you want to see the face poset in a graphical way, this is much easier. For example see this post:

https --- fix --- sheaves.github.io/Subgroup-Lattice/

and pay attention to the "plot" method of a Poset.

2 | No.2 Revision |

If by "visualize" you mean "give a geometric realization of" then I think that the answer should be "no" as I rather suspect that there are high-dimensional combinatorial polytopes that have no geometric realization. Even for three-dimensional polytopes the realization problem is ~~involved ~~delicate - there are even several layout algorithms for planar graphs. (There is at least one such implemented in sage - see:

http --- fix --- doc.sagemath.org/html/en/reference/plotting/sage/graphs/graph_plot.html

). On the other hand, if you want to see the face poset in a graphical way, this is much easier. For example see this post:

https --- fix --- sheaves.github.io/Subgroup-Lattice/

and pay attention to the "plot" method of a Poset.

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