# HW5
## Problem 1
  - 1.  - k = 4: tetrahedron
        - k = 5: F = 5, E = 7.5 (15 / 2), no dot exist
        - k = 6: two tetrahedron merge one facet with each other
  - 2.  - F = 4, E = 10, V = 8, not possible, total V must less than 7 (3 * 7 = 21 > 20)
        - F = 5, E = 10, V = 7, same reason
        - Yes, cube
  - 3.  - consider four side faces as a whole 5 by 3 face, and the top/down/inside faces as 1 by 1 faces
        - F = 4 + 21 * 2 + 4 * 8 + 12 + 8 + 4 = 102
        - E = 4 + 5 * 6 * 2 * 2 + 4 * 8 + 4 + 4 * 8 + 12 + 2 * 4 * 2 = 220
        - V = 6 * 6 * 2 + 4 * 8 = 104
        - Euler characteristic = 104 + 102 - 220 = -14
        - genus = (2 - (-14)) / 2 = 8 (-14 = 2 - 2g)
## Problem 2
  - 1.  ![2_1_1](2_1_1.png)
        - generated by [Ipe](https://ipe.otfried.org/)
        - Delaunay edges: 18
        - Voronoi edges: 18
        - |Q| = 1: 10
        - |Q| = 2: 18
        - |Q| = 3: 7
        - |Q| = 4: 2
        - |Q| = 5: 0
        - |Q| > 5: 0
  - 2.  ![2_2_1](2_2_1.png)