So far I have been doing this
3 consecutive days of
20 burpees x 2 1 minute planking x 3
and then rest
What is the recommended resting for me?
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Rest days are incorporated to give your body time to heal from activities that break down a lot of tissues or otherwise generate waste products.
A proper training plan will keep you on the edge of what you can just barely do and provide for enough rest that you will heal and progress.
While your workout is light years better than nothing, it's a far cry from a real training program. Your best bet is something that uses barbells, but if you're confined to just bodyweight there are programs out there as well.
A quick check to whether or not you need a rest day is if you can't do as much as you did the day before. Example: you do what you mentioned above on Tuesday, and then on Wednesday you can only knock out 15 burpees and you fall out of your plank before a minute is up. That's your body not being rested/repaired enough.
The odds are that the exercises you listed aren't nearly enough to cause your body to need 24 hours to repair.
Rest until your muscles stop feeling sore. If your muscles don't feel sore, increase intensity, duration, or sets.
Usually 1 day is a minimum between workouts that involve the same muscle groups, so you don't experience muscle loss or damage, but you can rest up to 5 days for larger muscle groups if they are still feeling sore.