The Platonic Solids


Dodecahedron

Icosahedron

Cube and Octahedron

Tetrahedron


My pages for the Platonic solids are going to be very simple. You will see the structures being tossed around by ocean waves and floating in marine tanks. The dodecahedron and icosahedron: both have 30 edges. With 20 vertices (vertex) and only 3 edges meeting at each of them, the dodecahedron comes closest to the volume of a sphere and appears to have the "softest" movements in breaking waves. Next is the icosahedron: with 5 edges meeting at each of 12 vertex, it is further from the shape of a sphere and its movements are more dramatic. A reference from a paper here relates that the icosahedron rolls the easiest, and there are many such references. There is no doubt that if sitting on a table, or riding out a swell, the pentagon faces of the dodecahedron are going to stay put over the icosahedron hands down. In breaking waves, however, the dodecahedron appeared to me to be as active as the icosahedron. The cube and octahedron: both have 12 edges. The cube, with its 90 degree angles, topples about and looks comical. The octahedron doesn't have the bluntness of the cube, so it isn't awkward, nor does it seem to twirl and spin around like its more spherical counterparts. The tetrahedron, stable and able to stay on one face the easiest, elegantly glides flat with edge-on orientation as though surfing, analogous to tetrahedral kites soaring through the sky.

Dodecahedron
Icosahedron
Hexahedron (the Cube)
Octahedron
Tetrahedron
and related structure: Rhombic Triacontahedron

Of course the degree of inflation (the structures are inflatables) makes a difference, and the intensity of the waves. What I have relayed is based on the experience of photographing them in real time and later looking at the photos, it is all heuristic, no research. What I need to do next time is videotape them in waves to examine movement over time instead of depending on unreliable memory and photographic stills. A question to consider is whether the same properties that hold true on a sturdy, flat surface, will remain true in turbulent water. One would think yes, and yet I watched what I recall to be a very active dodecahedron in breaking waves, not just once, or for one day, but on many different days, in spite of the fact that if "rolled" on a sturdy table, the dodecahedron would tend toward quickly landing on a face and staying there. On sand with a breeze behind it, the icosahedron gets away much faster than the dodecahedron. I had to chase them both down several times when they were sitting together on the sand.

Everything about the Platonic solids is uniform. They are the five regular polyhedra. Each one has a single shape and size for the faces, the same number of faces meet at each vertice, and all of the angles are the same across the surface. All other polyhedra are irregular (the snub octahedron, for instance, is made up of squares and hexagons) mixing different shapes for the faces and/or different sizes of the same shapes, and at least two different angles are present across the surface. In addition to the links above, you can also get around the site using the pulldown menu at the top of the page.


If you have questions about the pictures, please visit my FAQ page or contact me by email.


The image on this web page is © Copyright Gayla Chandler.
Permission must be sought for all but personal use for study or enjoyment.