The Violet triangle is an item used in The Eyes of Glouphrie and The Path of Glouphrie. It has a value of 21 in the Elven machine as calculated by multiplying the value of the shape's colour and the number of sides the shapes have. It can be found in Tree Gnome Village in a dungeon. You can get it if you find the key to set Golrie free. Search the chest and you'll find it.