Muddle 6 of the lychee in the cocktail shaker. Heavily muddle the lychee until it is broken down and juice is created. (If you prefer you could blend the lychee in a small food processor to create the juice.)
Fill the shaker with ice. Then add in the vodka, lemon juice, and orange liquor.
Put the lid on the shaker and shake vigorously.
Strain the contents from the shaker into a martini glass.
Garnish each glass with the remaining lychee.
Notes
We recommend chilling the martini glasses in the freezer for one hour before serving but this is purely optional.