0X0

XXX

0X0

0X0

But, you can also unwrap it in a zig-zag fashion, like so:

XX00

0XX0

00XX

How many ways can you unwrap a cube?

How many ways can you unwrap a cube with the caveat that each face is joined to 2 or fewer other faces?

How many ways can you unwrap an icosahedron?

How many ways can you unwrap an icosahedron with the caveat that each face is joined to 2 or fewer other faces?