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A topological geon is an asymptotically (anti-)de Sitter or flat spacetime with topology $\mathbb{R}\times M$, where $M$ is the punctured projective space, $M=\mathbb{R}P^3\backslash\{p\}$, and the removed point $p$ corresponds to the spacelike infinity. The manifold $M$ is conventionally obtained from a spherically symmetric spatial slice of a wormhole spacetime as the quotient manifold by the isometric action of the group $\mathbb{Z}_2$. We study the general properties of static, spherically symmetric, charged topological geons supported by a selfgravitating, minimally coupled scalar field with negative kinetic energy and an arbitrary selfinteraction potential. In the most general case, it turns out that the gravitational mass of such a geon is completely determined by its electric charge and size (for a given scalar field), that is, the size of the corresponding wormhole throat. We discuss the properties of the charged Ellis-Bronnikov-Sorkin geon and argue that it can be considered as a possible classical model of elementary particles beyond the Standard Model, in particular, as dark matter particles.