### Number of ways to unwrap a polyhedra

Posted:

**Tue Feb 02, 2010 11:14 pm**When we unwrap a cube, we usually elect to do it in such a way as to form a cross, like so:

0X0

XXX

0X0

0X0

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

XX00

0XX0

00XX

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?