The tetrahedron is created from four equilateral triangles, giving it 4 faces and 6 edges. It’s element is fire. The tetrahedron symbolizes willpower, courage, passion and self definition. It is associated with the fire signs Aries, Leo and Sagittarius.
The hexahedron or cube is six-sided created from 6 equal squares. It symbolizes the earth, stability, power and physical action. It is associated with the earth signs Capricorn, Taurus and Virgo. (See more cubes here)
The octahedron is created from 8 equilateral triangles, and thus has eight faces and 12 edges. It’s element is Air. This shape is symbolic of intellect, inspiration, new beginnings, and mental activity. Astrologically, the octahedron is connected to the air signs, Libra, Aquarious and Gemini.
The Number Eight: octagon, the supernatural creates cosmically committed energies, Magical Movement into the Astral Plane, Eternity. The Octahedron
The Icosahedron has twenty faces, being created by 20 equilateral trianngles with 30 edges. It’s element is Water. It symbolizes emotions, dreams and intuition. Astrologically, it is associated with the water signs Cancer, Scorpio and Pisces.
The Dodecahedron is composed of 12 faces with 30 edges. It’s element is Spirit. It symbolizes Divine connection, the universe, completion and wholeness. Astrologically, it is associated with the full zodiac.