Traditonally, the chakana (cruz cuadrada, meaning square cross in Spanish) represents the Southern Cross constellation, which the Andeans of old believed to be the center of the universe and was easily distinguished while gazing upon the night sky. The chakana held great significance to the Incan Empire and has numerous meanings in its design. Each of the three dimensional levels of the chakana are said to represent the three worlds, which in Quechuan, the Old Andean language, were called: Janan Pacha - Representing the Upper World/Above/Universe; Kay Pacha - Representing the Middle World /Here and; Now/Mother Earth; Ukju Pacha - Representing the Lower World/Inner Realms/Other World. Interestingly, these three worlds seem to correspond with the Holy Trinity; the Father, Son and Holy Spirit seen in Christianity, as well as the Body/Mind/Soul (Spirit) idea seen in Eastern Religions. The idea of there being an upper world, a middle world, and a lower world also correlates to many other world religions, such as the Norse view of Asgard, Midgard, and Hel.
The cultures of Machu Picchu had three spirit animals they felt symbolized the three worlds; the condor, the puma or jaguar, and the serpent. These correlate with the Andean cross of the Inca empire and what we know about how the chakana represents both a symbol of trinity and the Southern Cross. Symbols honoring spirit animals are found in many of the sacred sites and structures in the Andes. In fact, the city of Cusco, Peru, a city with old roots indeed, was built in the shape of a puma, showcasing the depth of culture that this particular symbol of the cross represents.
But there’s more than just sacred energy geometry in Cusco when it comes to the chakana cross and the symbology it represents. In addition to the Three Worlds, there are twelve steps that surround the chakana. Each of the twelve steps is said to represent a level of initiation and an attainment of consciousness. The chakana can also represent within its design the four cardinal directions as seen in a compass rose or cross: North, South, East and West. A chakana cross can also represent the four alchemical elements of Earth, Air, Fire, and Water.