Triangles represent the number 3 - the triality aspect. Nothing is really black or white and triality takes us out of duality thinking.
Amethyst: Often viewed as a stone of peace, some believe amethyst's calming presence produces soothing dreams by bringing the dreamer more in tune with the Divine. This clarity and peacefulness also extends to the waking mind. Amethyst is said to help the mind flow freely in both mental and metaphysical dimensions.