All Figures

	Figure 1: A sketch of the spatial distribution of the NBG galaxies in the Local Universe. The Sculptor-Coma cluster is highlighted and bigger dots are used for M 31, MW and the LG galaxies of 1. From Tully & Fisher (1988).
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In the text

	Figure 2: Hammer's projection with the amplitude of distortion (in percent) according to the code 1 = no distortion, 100 = extremely high distortion. The heavy dots are the galaxies of Table 1. The arrows indicate the regions of larger concentration of objects that could be interpreted as hints of underlying 3D structures. They, however, occur in regions of large distortion.
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In the text

Figure 3: Mercator's projection with Tissot's circles. The Mercator projection provides a good representation near the equatorial plane and a very poor one towards the poles. The lack of galaxies near the galactic plane is due to Galactic absorption. Clearly the apparent distribution is not uniform. There seem to be several 2D structures that could perhaps hint for real 3D structures. However, the same remark made in Fig. 2 would apply also here.

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In the text

	Figure 4: Cassini's projection with Tissot's circles. The North and South Galactic Poles are now well represented. Once again a few 2D structures can be noticed. They, however are located in regions of high distortion so that the same remark made in Fig. 2 would apply also here
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In the text

Figure 5: Projection onto the coordinate planes (X,Y) and (X,Z) as indicated, and two 3D views ( bottom left and right panels) of the our plane best minimizing the distance (location) of the LG galaxies. The (X,Y) projection ( top left panel) is parallel to the equatorial plane of the MW. The big red filled circles are MW and M 31. The yellow circles are the dwarf satellites on either sides of the plane. Looking at the 3D view in which the plane is seen edge-on ( bottom right), MW and M 31 are very close to it and within the uncertainty can be considered as belonging to it. See the text for details.

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In the text

	Figure 6: The 3D view of the three planes we have found with Eq. (7) together with the plane found by Sawa & Fujimoto (2005) seen edge-on and the galaxies of the LG. The two encircled zones highlight the position of MW and M 31 and their satellites. None of our planes coincides with that of Sawa & Fujimoto (2005). See the text for more details.
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In the text

Figure 7: 3D-view of the LG as observed from the same view angle adopted by Sawa & Fujimoto (2005), i.e. . The hatched plane is our best plane minimizing the distances and containing also MW and M 31. The red circles are MW and M 31, the yellow circles are the dwarf galaxies above the plane, whereas the dark circles are those below it. Once again the MW and M 31 groups are indicated. The straight line is the Sawa & Fujimoto (2005) plane seen edge-on. See the text for details.

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In the text

Figure 8: The two planes minimizing the spatial distribution of galaxies in the LG. One is the best plane derived from solving the system of Eq. (5) and given by the eigen-vectors of Eq. (7) that has already been presented, the other is obtained from the system of Eqs. (9) and the eigen-vectors of Eq. (10). This second solution assumes that the vector MW-M 31 lays on the plane. Within the uncertainty the two planes coincide.

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In the text

Figure 9: Orbits of the eight dominant galaxies or groups of galaxies derived from the minimization of the unconstrained action of Eq. (13). The orbits are shown as in Peebles (1989) for the sake of comparison. The orbits of MW and M 31 are highlighted. The circle has a radius , see Eq. (15) and the text for more details. We also tested the approximation adopted for the analytical representation of the orbits given by Eq. (17) with the equation of motion of Eq. (15). The corresponding orbits are nor shown as they in practice overlap with the present ones. Along each orbit a few selected stages are displayed: the initial stage at z=60, the stage at z=2 (the first circle), the stage at z=1 (the second circle) and the stage at the present time z=0 (the third circle).

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In the text

	Figure 10: Orbits of the galaxy groups and the two dominant galaxies derived from the constrained minimization of the action. The constraints are given by relations (27) and (28). The dots and circles along each orbit have the same meaning as in Fig. 9. The circles correspond to the present age.
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In the text

	Figure 11: Surfaces of constant gravitational potential for the galaxies and groups of galaxies given in Tables 3 and 2. The colour code makes it evident how the spherical symmetry dominates. The position of the LG is indicated.
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In the text

	Figure 12: The force field showing the radial behaviour of the streamlines of the MW and M 31 projected on the geometrical plane that minimizes the distances of the LG galaxies.
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In the text

	Figure 13: Top panel: face-on view of the plane minimizing the action and the geometrical distances of the LG galaxies together with the field line of the gravitational interaction exerted by the external galaxies on the LG. Bottom panel: the same but viewed edge-on. Note how the field lines are nearly parallel to the plane. See the text for more details.
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In the text

	Figure 14: The planes for the dwarf galaxies around the MW (Kroupa et al. 2005) and M 31 (Koch & Grebel 2006) compared to our plane. Unfortunately, we cannot show the plane of Sawa & Fujimoto (2005) as no equation for it has been given explicitly by the authors.
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In the text