Light curves, explosion energies, and remnant masses are calculated for a grid of supernovae resulting from massive helium stars that have been evolved including mass loss. These presupernova stars should approximate the results of binary evolution for stars in interacting systems that lose their envelopes close to the time of helium core ignition. Initial helium star masses are in the range 2.5 to 40,Msun, which correspond to main sequence masses of about 13 to 90,Msun. Common Type Ib and Ic supernovae result from stars whose final masses are approximately 2.5 to 5.6,Msun. For heavier stars, a large fraction of collapses lead to black holes, though there is an island of explodability for presupernova masses near 10,Msun. The median neutron star mass in binaries is 1.35--1.38,Msun and the median black hole mass is between 9 and 11,Msun. Even though black holes less massive than 5 Msun are rare, they are predicted down to the maximum neutron star mass. There is no empty ``gap, only a less populated mass range. For standard assumptions regarding the explosions and nucleosynthesis, the models predict light curves that are fainter than the brighter common Type Ib and Ic supernovae. Even with a very liberal, but physically plausible increase in $^{56}$Ni production, the highest energy models are fainter, at peak, than 10$^{42.6}$,erg,s$^{-1}$, and very few approach that limit. The median peak luminosity ranges from 10$^{42.0}$ to 10$^{42.3}$,erg,s$^{-1}$. Possible alternatives to the standard neutrino-powered and radioactive-illuminated models are explored. Magnetars are a promising alternative. Several other unusual varieties of Type I supernovae at both high and low mass are explored.
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