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Boxy/Peanut/X-shaped (B/P/X) bulges are studied using the 3.6 mum images fromthe Spitzer Survey of Stellar Structure in Galaxies, and the K_s-band imagesfrom the Near-IR S0 galaxy Survey. They are compared with the properties ofbarlenses, defined as lens-like structures embedded in bars, with sizes ofabout 50% of bars and axial ratios of 0.6-0.9. Based on observations and recentsimulation models we show evidence that barlenses are the more face-oncounterparts of B/P/X-shaped bulges. Using unsharp masks 18 new X-shapedstructures are identified, covering a large range of galaxy inclinations. Thesimilar masses and red B-3.6 mum colors of the host galaxies, and the fact thatthe combined axial ratio distribution of the host galaxy disks is flat, supportthe interpretation that barlenses and X-shapes are physically the samephenomenon. In Hubble types -3<T<2 even half of the bars contain either abarlens or an X-shaped structure. Our detailed 2D multi-componentdecompositions for 29 galaxies, fitting the barlens/X-shape with a separatecomponent, indicate very small or non-existent classical bulges. Taking intoaccount that the structures we study have similar host galaxy masses as theMilky Way (MW), our results imply that MW mass galaxies with no significantclassical bulges are common in the nearby Universe.

Milky Way mass galaxies with X-shaped bulges are not rare in the local Universe