Geodesic
Geometry of totally real Galois fields of degree~4
Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 1, pp. 33-44.

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We consider a totally real Galois field $K$ of degree 4 as the linear coordinate space $\mathbb Q^4\subset\mathbb R^4$. An element $k\in K$ is called strictly positive if all its conjugates are positive. The set of strictly positive elements is a convex cone in $\mathbb Q^4$. The convex hull of strictly positive integral elements is a convex subset of this cone and its boundary $\Gamma$ is an infinite union of $3$-dimensional polyhedrons. The group $U$ of strictly positive units acts on $\Gamma$: the action of a strictly positive unit permutes polyhedrons. Examples of fundamental domains of this action are the object of study in this work. 
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Yu. Yu. Kochetkov. Geometry of totally real Galois fields of degree~4. Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 1, pp. 33-44. http://geodesic.mathdoc.fr/item/FPM_2014_19_1_a3/

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