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A finite field is a field with a finite number of elements. For each prime power $q^k$, there is a unique (up to isomorphism) finite field with $q^k$ elements. Up to isomorphism, these are the only finite fields.

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Grothendieck on polyhedra over finite fields

Not an exact answer to your question but maybe it can be helpful to know: La théorie combinatoire de l'icosaèdre by V Diekert This was a "Rapport pour un DES d'université de l'année 1977/78" under Gro …
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