# Constructing Path Connected Space

## Homework Statement

1. Construct a path connected space X such that the fundamental group of (X,x_0)
where x_0 is the base point; such that the fundamental group is the symmetric
group on 3 letters?

2. Let Z be the space obtained from a hollow cube by deleting the interior of its
faces. Compute fundamental group of (Z,z_0) where z_0 is a basepoint.

## The Attempt at a Solution

Both problems seem very related; I believe if I can solve one of them I can mostly like use similar ideas to solve the other. It seems like it must admit a simple solution; a graph of some sort. But I cannot spot any at the moment