Problem Level Platonic Solid

[mdm]

Since all five platonic solids are used in the five problem level pictures, what's the plan for the next picture when we get to Level Six?

[Tommy137]

Since all five platonic solids are used in the five problem level pictures, what's the plan for the next picture when we get to Level Six?

Just wait and see (and solve)

[JohnMorris]

Just count the sides of the five that are there and pretend it's one of those "what's the next number in this sequence" problems.

4, 6, 8, 12, 20, ??

Since this is clearly the function n³/3 - n² + 8n/3 + 4, for n = 0..4, the next one must have 34 sides. So it's going to be a heptadecagonal trapezohedron.

[genious999]

Here I was hoping it would be hyperdodecahedron...

[Tommy137]

As a soccer fan, I obviously would prefer the truncated icosahedron

[genious999]

Truncated icosahedrons are cool, too. I've made several origami truncated icosahedrons, and everybody I know says they are amazing. The only difficult part about making them is coordinating the 3 colors of paper so that each vertex has exactly one edge of each color connecting it. Would there be an "easy" way to do that?

[Georg]

I'd like to go 4D.

[pjt33]

Another obvious extension is the regular "solids" of infinite volume. There are three, with respectively 6 triangles, 4 squares, or 3 hexagons meeting at each vertex, and tiling the surface of an infinitely large sphere.