Most of the illusions we hear about and enjoy playing with are optical illusions. This is a tactile illusion.
To experience this illusion, all you need is a marble or a pea. Cross your fingers, extending the middle finger over the index finger so the two fingertips are next to each other, but reversed from their normal arrangement. Now roll the marble around on a table with your crossed fingertips. Almost immediately you'll probably get the distinct impression that there are two marbles, not just one.
Crossing your fingers makes information travel to your brain through unusual channels. Normally the outside of your middle finger and the inside of your index finger face away from each other. Crossing your fingers brings those two sides together. When the marble gets between your crossed fingertips, it touches areas that normally would be touched only if there were two marbles. Cross your fingers, and one marble feels like two.
This effect has been known long enough to be called Aristotle's illusion. Here are some modern variations.
Try using your nose instead of a marble. Your fingertips may give you the impression that you have two noses.
Try different fingers: cross your middle finger over your ring finger. Then lay a pencil over the two crossed fingertips so the barrel of the pencil touches one fingertip and the point touches the other. See if you can tell, just by touch, which way the pencil is pointing. Rocking the pencil gently back and forth may enhance the strangeness and vividness of the sensation.