In Euclidean geometry, a Platonic solid is a regular, convex polyhedron. The faces are congruent, regular polygons, with the same number of faces meeting at each vertex. There are five Platonic solids; their names are derived from their numbers of faces.
The aesthetic beauty and symmetry of the Platonic solids have made them a favorite subject of geometers for thousands of years. They are named for the ancient Greek philosopher Plato, who theorized that the classical elements were constructed from the regular solids.
According to Stephen Skinner, the study of sacred geometry has its roots in the study of nature, and the mathematical principles at work therein. Many forms observed in nature can be related to geometry, for example, the chambered nautilus grows at a constant rate and so its shell forms a logarithmic spiral to accommodate that growth without changing shape. Also, honeybees construct hexagonal cells to hold their honey. These and other correspondences are seen by believers in sacred geometry to be further proof of the cosmic significance of geometric forms. These phenomena can be explained through natural principles.
Amethyst is the purple variety of quartz crystal composed of silicon dioxide with traces of iron.
As a healing stone it is said to be helpful in ridding nightmares. Just hold the Amethyst crystal on the forehead for a minute and ask it to guide you through a peaceful sleep, then place it under your pillow. Also helpful to calm an overworked and over stressed mind. It is thought to dispel negativity and create a peaceful environment.