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We explore the Papadodimas–Raju prescription for reconstructing the region behind the horizon of one-sided black holes in AdS/CFT in the case of the $\mathbb{R}{{{\rm P}}^{2}}$ geon—a simple, analytic example of a single-sided, asymptotically AdS3 black hole, which corresponds to a pure CFT state that thermalizes at late times. We show that in this specific example, the mirror operators involved in the reconstruction of the interior have a particularly simple form: the mirror of a single trace operator at late times is just the corresponding single trace operator at early times. We use some explicit examples to explore how changes in the state modify the geometry inside the horizon.