Geodesic
Inflation and deflation of the karyon tilings
Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 6, Tome 523 (2023), pp. 53-82

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The substitution transformations of inflation and deflation are defined for the karyon tilings $\mathcal{T}(v)$ of multidimensional tori $\mathbb{T}^d$. Such tilings $\mathcal{T}(v)$ consist of parallelepipeds and are generated by its karyons. Stars $v$, sets of $d+1$ vectors in the space $\mathbb{R}^d$, are frames of the karyons. The interest in karyon tilings is due to their connections with multidimensional continued fractions. 
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     author = {V. G. Zhuravlev},
     title = {Inflation and deflation of the karyon tilings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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V. G. Zhuravlev. Inflation and deflation of the karyon tilings. Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 6, Tome 523 (2023), pp. 53-82. http://geodesic.mathdoc.fr/item/ZNSL_2023_523_a4/