Hello World,

First off, because I lack a 3-D Modeling Program, I decided to use the 2-D Representations of the Platonic Solids. Sinse they are meant to fit into a sphere I placed them all in a sphere. 384 more words

Hello World,

First off, because I lack a 3-D Modeling Program, I decided to use the 2-D Representations of the Platonic Solids. Sinse they are meant to fit into a sphere I placed them all in a sphere. 384 more words

Since I named my blog after the last of the platonic solids; (regular, convex polyhedrons) the 20 triangular-faced icosahedron, I thought that I would explain why for my first post. 210 more words

https://www.mathsisfun.com/platonic_solids.html

A Platonic Solid is a 3D shape where:

- each face is the same regular polygon
- the same number of polygons meet at each vertex (corner) 156 more words

http://moirenike.tumblr.com/post/127255329467/a-student-balancing-the-platonic-solids-can-you

A funny sketch about the platonic solids…I guess they aren’t ready for a commitment then.

The G19 Artisan Gallery is located in Rockport, Massachusetts. Rockport is a picturesque town known for its art community for almost one hundred years. Historically, Rockport artists are known for their seascapes, but the G19 gallery exhibits art in a wide range of materials, styles and themes. 244 more words

This is the hyperdodecahedron, or 120-cell, one of the six four-dimensional analogs of the Platonic solids. It’s been shown on this blog before, but this image has one major change: a much slower rotational speed. 39 more words

Here's an engaging moving picture from RobertLovesPi. The Platonic solids --- cubes, pyramids, octahedrons, icosahedrons, and dodecahedrons --- are five solid shapes each with the same regular convex polygon as their face. This is a nice two-dimensional rendering of a three-dimensional projection of a ``hyperdodecahedron''. It's made of 120 dodecahedrons, in a four-dimensional space. And it's got the same kind of structure that Platonic solids have, being made of the same regular convex polyhedron for each face.
Remarkably, I learn from Mathworld, the shape is three-colorable. That is, suppose you wanted to assign colors to each of the corners in this four-dimensional shape. They're all green circles here, but they don't have to be. There are a *lot* of these corners, and they're connected in complicated ways to one another. But you could color in every one of them, so that none if them is connected directly to another of the same color, using only three different colors.