1. TOAST Toroidiality

2. Starting with the TOAST parameterization: We unfold it to get: B C G F H E A D E H B C F G

3. This parameterization tiles horizontally: And vertically (after 180o rotation): G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C

4. Putting all this together, we can get:F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C

5. Giving a toroidal tiling:F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C G F H E A D B C