Phyllis Sidhe_Uaine said:
Actually, Louis, the inverted penticle also symbolizes (in some Wiccan traditions) a second-degree practitioner (please correct me if I'm wrong any of the Wiccan practitioners on this board.)
The inverted star clearly represents a man falling into the abyss (the single point representing the head, the two opposite representing the legs). It is unfortunate that people use it to mean something else, believing that because they view it as something good, it is. This is because geometrical forms are objective and it does not matter what one thinks it means -- it is what it is. Man himself is the pentacle. Obviously the upright pentacle represents the ascension of man.
This is not to say that we must descend before we ascend, by all means we must, as it is shown in any hero's journey -- as they always go into Hell before Heaven. This is the true meaning of the inverted cross, the Cross of Peter, which is why Dante's Inferno has a lot with St. Peter. The Keys of Peter are the gateway into Hell, the very path that leads to Heaven.
Returning to the topic, the geometrical form of the swastika holds tremendous power. In a very synthetic form it means the movement of the universe, the endless movement of the energy. The swastika is nothing more than the cross in movement. The cross itself is the intersection of opposites: Positive & Negative, Man & Woman, Ying & Yang, Ida & Pingala, Shiva & Shakti, Creation & Destruction, Proton & Electron, etc. The movement therefore represents the Third Force, the synthesis of the first two, the reconciliation, Neutron. It is the sustainment of the energy to exist in order to prevent it from returning to the Nothingness, because all energy is entropic and without a host to facilitate its eternal becoming it becomes-not, a Nothing (called the Adi-Buddha, Tao, Sat, Ain, Omeyocan, in various traditions).
The swastika very closely represents the spiral galaxy we live in, and this something we can spend time meditating upon.