Geodesic
On the geometry of two- and three-dimensional Minkowski spaces
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 5, Tome 267 (2000), pp. 146-151

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A class of centrally-symmetric convex 12-topes (12-hedrons) in $\mathbb R^3$ is described, such that for an arbitrary prescribed norm ${\|\cdot\|}$ on $\mathbb R^3$ each polyhedron in the class can be inscribed in (circumscribed about) the ${\|\cdot\|}$-ball via an affine transformation, and this can be done with large degree of freedom. It is also proved that the Banach–Mazur distance between any two two-dimensional real normed spaces does not exceed $\ln(6-3\sqrt2)$. 
@article{ZNSL_2000_267_a8,
     author = {V. V. Makeev},
     title = {On the geometry of two- and three-dimensional {Minkowski} spaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {146--151},
     publisher = {mathdoc},
     volume = {267},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_267_a8/}
}
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V. V. Makeev. On the geometry of two- and three-dimensional Minkowski spaces. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 5, Tome 267 (2000), pp. 146-151. http://geodesic.mathdoc.fr/item/ZNSL_2000_267_a8/