Geodesic
The reconstruction of Platonic solid from its rib
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 34, Tome 478 (2019), pp. 194-201 
B. B. Lur'e. The reconstruction of Platonic solid from its rib. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 34, Tome 478 (2019), pp. 194-201. http://geodesic.mathdoc.fr/item/ZNSL_2019_478_a8/
@article{ZNSL_2019_478_a8,
     author = {B. B. Lur'e},
     title = {The reconstruction of {Platonic} solid from its rib},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {194--201},
     year = {2019},
     volume = {478},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_478_a8/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider the problem of reconstruction of Platonic solid with integer coordinates of vertices when its edge (or the diagonal of the cube) is given. We find the necessary and sufficient conditions of existence of such polyhedrons as well as the algorithm of construction and the number of solutions.

[1] R. O. Kuzmin, D. K. Faddeev, Algebra i arifmetika kompleksnykh chisel, Uchpedgiz, L., 1939