Neostylopyga rhombifolia (Harlequin Cockroach)

Housing:

Something about a gallon in size works well for a starter culture, large colonies would likely prefer something more like 5 gallons or larger for a permanent setup. An airtight lid or climbing barrier is a must, as all life stages can climb. High ventilation levels are preferred. 
For substrate, an inch or so of coconut fiber, potting soil, etc. should be used, topped with lots of hides in the form of bark, eggcrates, cardboard rolls, etc.. 
This species prefers semi-humid conditions, so a 60-40 humidity gradient works fine, erring on the drier side. Their oothecae are pretty tolerant of dryness but need some moisture to hatch, so misting the entire enclosure lightly every now and then is encouraged. 

Diet:

Dog/cat/fish food, fruits and veggies works as the staple diet.

Temperature:

Temps in the 75-85F° range are preferred for breeding and optimal growth rates.

Breeding/Life Cycle:

Adults live 4-6 months on average, and lay oothecae once or twice a week, which take 2-3 months to hatch. Nymphs take 4-6 months to mature under optimal conditions. Adults and perhaps larger nymphs of this species can produce a strong tasting chemical defense that smells a bit like almond/cherry extract, so are not a suitable feeders for vertebrates. But invertebrates are unaffected by the defense fluid. This species is very prolific, and so is well suited for at least occasional feeder use.

It should be noted that a lot of strains of this species can be prone to random colony crashes, or are very picky about humidity levels. However, the Chinese hobby stock of this species is very hardy, and has gained a strong foothold in the US hobby now.