The biggest criticisms of existing theories that describe the building blocks of spacetime as a cosmological polytope are:

- They are not yet experimentally verified. While there is some mathematical evidence to support the idea of cosmological polytopes, there have been no direct experimental tests of these theories.
- They are difficult to reconcile with general relativity. General relativity is our current best theory of gravity, and it does not seem to be compatible with the idea of cosmological polytopes.
- They are not yet fully understood. The mathematics of cosmological polytopes is very complex, and there are many aspects of these theories that are not yet fully understood.

Despite these criticisms, cosmological polytopes remain an intriguing possibility for a theory of the building blocks of spacetime. If they are correct, they could provide a new way to understand the universe and its origins.

Here are some additional details about each of these criticisms:

- Experimental verification: There have been some experimental tests of cosmological polytope theories, but these tests have not been conclusive. For example, one test looked for evidence of cosmological polytopes in the cosmic microwave background radiation, but the results were inconclusive. More experimental tests are needed to confirm or refute the existence of cosmological polytopes.
- Compatibility with general relativity: General relativity is our current best theory of gravity, and it does not seem to be compatible with the idea of cosmological polytopes. General relativity predicts that spacetime is smooth and continuous, while cosmological polytopes suggest that spacetime is made up of discrete building blocks. This is a major challenge for cosmological polytope theories, and it is not yet clear how to reconcile these two theories.
- Lack of understanding: The mathematics of cosmological polytopes is very complex, and there are many aspects of these theories that are not yet fully understood. This makes it difficult to test these theories experimentally and to develop them further.

Despite these challenges, cosmological polytopes remain an intriguing possibility for a theory of the building blocks of spacetime. If they are correct, they could provide a new way to understand the universe and its origins.
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