This looks to be a M42 mount lens. The "Dimension" brand was probably a store-label brand made by Sun, Cosina, Chinon, or some such other lensmaker. ("Dimension" is unfortunately a horrible name to Google for...)

This thread at MFLenses Forums apparently covers the exact same lens model (it's old enough that a lot of the image links are broken). Apparently it's a very decent lens.

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Note: Michael Clark helpfully suggested to mention the similarity between the M42 mount and the T-mount. Both mounts are 42mm threads.

• The M42 mount has a 1mm thread pitch; thus, it's more fully specified as M42×1.
• The T-mount has a 0.75mm thread pitch; thus, it's more fully specified as M42×0.75.

If the thread pitch doesn't stand out as an obvious distinction (it can be hard to tell the difference), another possible giveaway is the aperture pin: although Sigma's YS mount (which was based on the T-mount) had an aperture pin, many more M42-mount lenses had aperture pins than YS-mount lenses did. Of course, not all M42-mount lenses had aperture pins, so you're back to measuring thread pitch.

Takeaway: make sure to measure the thread pitch before assuming M42.

See also: the accepted answer to How do I identify unknown thread mounts?