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[caption id="attachment_78" align="alignright" width="249"] Sketch of the time-space model with a conic time space surface limited by the shoreline of an island (L'Hostis 2016 CC-BY)[/caption]This is how it will look like when the model will be complete. Time-space is represented by cones. As explained here, the slope of the cone allows to produce longer itineraries proportionally to the maximum available speed on the space considered.Then two issues must be resolved, one theoretical, and the other more linked to graphic and cartographic choices. Firstly this is a terrestrial time-space, and the surface should not extend in the maritime domain, where different transport conditions occur. Secondly, these representations have a major issue to overcome: the readability of the representation in reference to the conventions of classical maps. This second arguments implies to render shorelines and continents shapes in order to make the representation more easy to read.For these two reasons the basic cone structure will be cut along shorelines, as in this example of an island carrying a city. It remain to be decided, judging again by the criterion of legibility, if the final structure will be a volume or a surface.