Too long for a comment. I did a search in French and German but it didn't help much. I think this might have to do with the topic of "polyhedra over finite fields".
Someone asked the same question in French here. The answers like to a post by user Mauricio (answering a question about what Grothendieck had to do with the icosahedron) which says:
Grothedieck a exploré plusieurs facettes du problème. L'une
d'entre-elle est le théorème de Brieskorn-Grothendieck. Klein dans son
livre sur l'icosaèdre à montré qe si tu prends un polyèdre régulier et
que tu relèves son groupe de symétrie dans SU(2), tu obtiens un groupe
dont l'algèbre des invariants est celui d'une variété singulière. Tu
retrouves comme ça les singularités A,D,E. Une bonne référence est
simplement Klein.
(see the link for more)
Grothendieck explored several facets of the problem. One of them is
the Brieskorn-Grothendieck theorem. Klein in his book on the
icosahedron showed that if you take a regular polyhedron and lift its
symmetry group into SU(2), you obtain a group whose algebra of
invariants is that of a singular variety. You thus find the A, D, E
singularities. A good reference is simply Klein.
However, I don't think this is what the Wikipedia article means. There is also another MathOverflow question on the topic of Grothendieck and polyhedra which seems closer to what you are looking for.
In Grothendieck's Sketch of a Programme he spends a few pages
discussing polyhedra over arbitrary rings and concludes with some
intriguing remarks on specializing polyhedra over their "most singular
characteristics". I am having trouble understanding what he means or
finding other references.
You may find further information in the comments and answer to that question. Here is a link to a 2023 paper which attempts to understand and interpret what he was talking about (the case of polyhedra over finite fields).
