series: Platonic Solids

The more that I learn about the Platonic Solids, the more interesting I find them.  You may remember something about the solids from this post about the inspiration behind my stained glass series, but this past week I found out more about their relationship with the historic four elements: fire, earth, air and water.

The mathematical laws governing the tetrahedron, cube, and dodecahedron were first studied about 2500 years ago by the Pythagoreans. 

Later, the Greek mathematician Theaetetus (415 - 396 B.C.) came up with a mathematical postulation for the octahedron and icosahedron, as well as proof that only five Platonic solids exist.

However, the Greek philosopher Plato (428 - 348 B.C.) (for which the solids get their name) described the solids in detail in his book “Timaios” and allotted them to the four basic elements within the Platonic world view. These are: fire, water, air and earth.  The dodecahedron was added later as a ‘fifth’ element, embodying the universe.

(Besides sharing some more of my creative process, I really I wanted an excuse to use these cool rotating images below!)

The tetrahedron (greek “tetráedron” = four-sided) is bounded by 4 regular triangles and has 6 edges of equal length.  Three triangles meet at each of the vertices.  According to Plato it symbolizes dryness or fire (hot & dry).

The cube (in greek hexahedron “hexáedron” = six-sided) is bounded by 6 squares and has 12 edges of equal length. Three squares meet at each of the vertices.  It stands firmly on its base and ccording to Plato it stands for the stable earth.

The octahedron (greek “oktáedron” = eight-sided) is bounded by 8 equilateral triangles and has 8 edges of equal length. Four triangles meet at each of the vertices. It can rotate freely when grasped at opposite vertices and symbolizes air.

The dodecahedron (greek “dodécáedron” = twelve-sided) is bounded by 12 regular pentagons and has 30 edges of equal length. Three pentagons meet at each of the vertices. It represents the universe and, according to Plato, its faces symbolize the 12 signs of the zodiac.

The icosahedron (greek “eikosáedron” = twenty-sided) is bounded by 20 equilateral triangles and has 30 edges of equal length.  Five triangles meet at each of the vertices. According to Plato, it symbolizes water.





How interesting are these shapes?  I think it would be really neat to match up the shapes with your zodiac sign.  For example, I'm a Capricorn, which is an earth sign, so the cube would be my match.  I think that the next solid I make for myself will definitely be a cube in earthy tones.  I matched up the shapes and signs below in case you want to see what you would be!

• Tetrahedron/Fire signs (Aries, Leo, and Sagittarius)
• Cube/Earth signs (Taurus, Virgo, and Capricorn)
• Octahedron/Air signs (Gemini, Libra, and Aquarius)
• Icosahedron/Water signs (Cancer, Scorpio, and Pisces)

P.S. After reading about all of this I made up a special stained glass "elements" series, which has the five shapes in miniature sizes.  I made each shape in the colors of the element is symbolizes.  I'll upload a photo on Friday!


Images & some content courtesy of 3Quarks - Platonic Solids