1 The numbers on opposite faces of the die shown (a standard die) add up to 7. The adjacency graph for the die is a graph which has vertices representing faces. In the adjacency graph two vertices are joined with an arc if they share an edge of the die. For example, vertices 2 and 6 are joined by an arc because they share an edge of the die.
\includegraphics[max width=\textwidth, alt={}, center]{dab87ac5-eda4-433f-b07a-0a609aca2f65-2_246_213_488_1608}

1. List the pairs of numbers which are opposite each other.
2. Draw the adjacency graph.
3. Identify and sketch a solid which has the following adjacency graph.
   \includegraphics[max width=\textwidth, alt={}, center]{dab87ac5-eda4-433f-b07a-0a609aca2f65-2_287_307_1027_879}