Probably something that's mostly saturated since that's the most common fatty acids found in animals
Coconut. Or maybe lard. But probably not lard (though I think that's what soap used to be made with).
i LOVE mixing a cup of cacao butter and a cup of coconut oil on the stove top until melted. i add in about 20 drops of peppermint essential oil to make mint chocolate whipped butter. let the mixure sit in the fridge for about 30- 45 minutes (not solid but gloopy) and then whip it with a hand blender. i rub this on my skin after i shower and i smell like a york peppermint patty.
The Himba tribe of Namibia have women with the most beautiful skin I have seen, and this is amongst a group of hard working women living outdoors in the African sun. They daily rub their skin with a mixture of red clay along with butter or animal fat. Of course this isn't practical in the western world so I would go with the closest thing, a plant derived saturated fat, and in particular the anti-microbial compounds found in tropical oils would prove useful for skin. Unrefined palm oil would leave your skin red so that narrows it down to an extra virgin coconut oil. I personally use extra virgin coconut oil on my face and body, and I have clear moisturized skin.
My favorite so far is apricot oil.
Gives a wonderful texture and glow, and doesn't make the skin look greasy. I use it as a day/night cream. Good instead of any body lotion, too, you don't need a huge amount of it. Great on the hands as well, absorbs quickly.
I use coconut oil and love it. A tiny bit goes a long way and sometimes you'll need to towel it off a bit. I've known people to use coconut oil with great success - it absorbs well for them. But others end up being greasy so I'd test a small area first and see how that goes.
I also use coconut oil as a makeup remover and on the ends of my hair as a leave in conditioner. It's truly a multi-purpose and inexpensive beauty product!
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