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We report on figure-eight choreographic solutions to a system of threeidentical particles interacting through a potential of Lennard-Jones type,$1/r^{12}-1/r^6$ where $r$ is a distance between the particles. By numericalsearch, we found there are a multitude of such solutions. A series of them areclose to a figure-eight solutions to a homogeneous system with no $1/r^{12}$term in the potential. The rest are very different from them and have severalpoints with large curvatures in their figure-eight orbits, at which particlesare repelled. Here figure-eight choreographies are the periodic motion whoseshape is symmetric in both horizontal and vertical axis, starting with anisosceles triangle configuration and going back to an isosceles triangleconfiguration with opposite direction through Euler configuration. Thus thelobe of this figure-eight may be complex shape and needs not to be convex.

Figure-eight choreographies of the equal mass three-body problem with Lennard-Jones-type potentials