26 lines
1009 B
Markdown
26 lines
1009 B
Markdown
# HW5
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## Problem 1
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- 1. - k = 4: tetrahedron
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- k = 5: F = 5, E = 7.5 (15 / 2), no dot exist
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- k = 6: two tetrahedron merge one facet with each other
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- 2. - F = 4, E = 10, V = 8, not possible, total V must less than 7 (3 * 7 = 21 > 20)
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- F = 5, E = 10, V = 7, same reason
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- Yes, cube
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- 3. - consider four side faces as a whole 5 by 3 face, and the top/down/inside faces as 1 by 1 faces
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- F = 4 + 21 * 2 + 4 * 8 + 12 + 8 + 4 = 102
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- E = 4 + 5 * 6 * 2 * 2 + 4 * 8 + 4 + 4 * 8 + 12 + 2 * 4 * 2 = 220
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- V = 6 * 6 * 2 + 4 * 8 = 104
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- Euler characteristic = 104 + 102 - 220 = -14
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- genus = (2 - (-14)) / 2 = 8 (-14 = 2 - 2g)
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## Problem 2
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- 1. 
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- generated by [Ipe](https://ipe.otfried.org/)
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- Delaunay edges: 18
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- Voronoi edges: 18
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- |Q| = 1: 10
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- |Q| = 2: 18
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- |Q| = 3: 7
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- |Q| = 4: 2
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- |Q| = 5: 0
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- |Q| > 5: 0
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- 2.  |