## Stony Brook University MAT 118 Spring 2013

### Assignment 6 due in Recitation, week of March 11

1. Mindscape 4 on page 284.
2. Mindscape 15 on page 285.
3. The polyhedron shown in Mindscape 30 (page 288) can be derived from a red dodecahedron by replacing each edge with a yellow square and each vertex with a blue triangle.
1. Use this remark as a hint and calculate the total number of faces of the "small rhombicosidodedahedron," as it is called.
2. Count the number of vertices and edges of this solid.
3. Describe the dual of this polyhedron. How many faces does it have and what do they look like?
4. Draw a graph of your own with at least five vertices, at least one loop, at least one double edge and at least one "peninsula" edge (see page 419). Using a different color, draw the dual of your graph. Draw another copy of your dual, and, using a different color, draw its dual. Check that the last graph you obtain is the same as the one you started with.
5. Mindscape 9 on page 429.
6. Mindscape 21 on page 431.