(Abridged). The cataclysmic binary V405 Peg, originally discovered as ROSAT Bright Source (RBS) 1955 (= 1RXS J230949.6+213523), shows a strong contribution from a late-type secondary star in its optical spectrum, which led Schwope et al. to suggest it to be among the nearest cataclysmic binaries. We present extensive optical observations of V405 Peg. Time-series spectroscopy shows the orbital period, Porb, to be 0.1776469(7) d (= 4.2635 hr), or 5.629 cycle/d. We classify the secondary as M3 - M4.5. Astrometry with the MDM 2.4m telescope gives a parallax 7.2 +- 1.1 milli-arcsec, and a relative proper motion of 58 mas/yr. Our best estimate of the distance yields d = 149 (+26, -20) pc. The secondary starss radial velocity has K2 = 92 +- 3 km/s, indicating a fairly low orbital inclination if the masses are typical. Extensive I-band time-series observations in the show the system varying between a minimum brightness level of I = 14.14 and states of enhanced activity about 0.2 mag brighter. While the low-state shows an ellipsoidal modulation, an additional photometric modulation appears in the high state, with 0.1 mag amplitude and period 220-280 min. The frequency of this modulation appears to be stable for a month or so, but no single period was consistently detected from one observing season to the next. We estimate the system luminosity by combining optical measurements with the archival X-ray spectrum. The implied mass accretion rate is orders of magnitudes below the predictions for the standard angular momentum loss above the period gap. The system may possibly belong to a largely undiscovered population of hibernating CVs.
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