This gives the complete list of names of polyhedra that are known to the Wolfram Language:

Choose one polyhedron name at random. Rerun the code to get a different choice:

Wrap the randomly chosen polyhedron name with PolyhedronData to get a picture of it:

This gives a graphic of a dodecahedron:

You can get the same result by asking for the GraphicsComplex of the dodecahedron and providing a Graphics3D wrapper:

GraphicsComplex gives the vertices and polygons indexed in terms of those vertices for a 3D graphics object:

The advantage of supplying the Graphics3D wrapper yourself is that you can put more than one polyhedron into the graphic.

This makes a graphic of 100 polyhedra chosen at random. They’re all positioned in the same place, so they intersect:

Add a translation to spread out the random polyhedra.

This gives a random number between 0 and 20:

This gives three random numbers:

Put each polyhedron at a random position, using RandomReal to generate a random 3D coordinate:

RandomColor gives a random color. Rerun the code to get a different choice:

Give each polyhedron a random color (you need to put the color and the polyhedron in a list, indicated by curly brackets):

Deploy the “polyhedron party” code to the Wolfram Cloud, where anyone with a browser can use it:

Click the link in the output to visit the site. Refresh the page in your browser to get a new image.

Tell the world about your creation by sharing the link via email, tweet or other message.