---
abstract: |
    In tropical geometry, one studies algebraic curves using combinatorial techniques via the tropicalization procedure. The tropicalization depends on a map to an algebraic torus and the combinatorial methods are most useful when the tropicalization has nice properties. We construct, for any Mumford curve $X$, a map to a three dimensional torus, such that the tropicalization is isometric to a subgraph of the Berkovich space ${X^{\rm an}}$, called the extended skeleton.

    MSC: Primary: 14T05; Secondary: 14G22, 32P05

    Keywords: Tropical geometry, smooth tropical curves, Mumford curves, extended skeleta, faithful tropicalization
address:
- 'Trevor Gunn, School of Mathematics, Georgia Institute of Technology, Atlanta, USA'
- 'Philipp Jell, Universität Regensburg, 93040 Regensburg'
author:
- Trevor Gunn
- Philipp Jell
bibliography:
- 'Effective-Fully-Faithful.bib'
title: Construction of Fully Faithful Tropicalizations for Curves in Ambient Dimension 3
---

Introduction
============

It is a well-known classical fact that while not every algebraic curve is a plane curve, every curve is a space curve. That is, every curve admits a closed embedding into ${\mathbf{P}}^3$ (see for instance [@Har Corollary IV.3.6]). Similarly, every graph has an embedding in ${\mathbf{R}}^3$. In fact, this can be done with straight lines by putting the vertices as points on the twisted 