The Five Platonic Solids
The Five Platonic Solids
The five platonic solids are the tetrahedron, cube, octahedron, dodecahedron, and a icosahedron.
They are named for the greek philosopher Plato. Plato wrote about them in the Timaeus (c.360 B.C.) in which he paired each of the four classical elements earth, air, water, and fire with a regular solid. Earth was paired with the cube, air with the octahedron, water with the icosahedron, and fire with the tetrahedron. The fifth Platonic solid, the dodecahedron, Plato says that, "...the god used for arranging the constellations on the whole heaven".
Aristotle later added a fifth element, the aether and postulated that the heavens were made of this element, but he had no interest in matching it with Plato's fifth solid.
Euclid completely described the Platonic solids in the Elements, the last book to be …show more content…
All 6 faces are flat and straight and all 12 edges touch and are straight as well. The cube is paired with earth.
The octahedron: The octahedron is composed of eight equilateral triangles, four of which meet at each vertex and having three pentagonal faces around each vertex. It looks as if four pyramids have been combined and are magnetically stuck together. The octahedron is paired with air.
The dodecahedron: The dodecahedron has 20 vertices, 30 edges, 160 diagonals and 12 faces. Three of the faces meeting at each vertex. The dodecahedron looks like a pointy circle. The dodecahedron isn’t paired with an element.
The icosahedron: The icosahedron has 20 faces, 30 edges and 12 vertices. It has five equilateral triangular faces meeting at each vertex. The icosahedron is paired with water.
For a solid to be considered a platonic it needs each face to be a regular polygon and each vertex must come together because if only two came together the figure would collapse on itself. The sum of each interior angle of the faces meeting at a vertex must be less than 360
The five platonic solids are the tetrahedron, cube, octahedron, dodecahedron, and a icosahedron.
They are named for the greek philosopher Plato. Plato wrote about them in the Timaeus (c.360 B.C.) in which he paired each of the four classical elements earth, air, water, and fire with a regular solid. Earth was paired with the cube, air with the octahedron, water with the icosahedron, and fire with the tetrahedron. The fifth Platonic solid, the dodecahedron, Plato says that, "...the god used for arranging the constellations on the whole heaven".
Aristotle later added a fifth element, the aether and postulated that the heavens were made of this element, but he had no interest in matching it with Plato's fifth solid.
Euclid completely described the Platonic solids in the Elements, the last book to be …show more content…
All 6 faces are flat and straight and all 12 edges touch and are straight as well. The cube is paired with earth.
The octahedron: The octahedron is composed of eight equilateral triangles, four of which meet at each vertex and having three pentagonal faces around each vertex. It looks as if four pyramids have been combined and are magnetically stuck together. The octahedron is paired with air.
The dodecahedron: The dodecahedron has 20 vertices, 30 edges, 160 diagonals and 12 faces. Three of the faces meeting at each vertex. The dodecahedron looks like a pointy circle. The dodecahedron isn’t paired with an element.
The icosahedron: The icosahedron has 20 faces, 30 edges and 12 vertices. It has five equilateral triangular faces meeting at each vertex. The icosahedron is paired with water.
For a solid to be considered a platonic it needs each face to be a regular polygon and each vertex must come together because if only two came together the figure would collapse on itself. The sum of each interior angle of the faces meeting at a vertex must be less than 360