 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ib/paper-2/11g/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

For

T^{2}

[0, 1] \times [0, 1]

. Identify

(0, y) \sim (1, y), (x, 0) \sim (x, 1),

so both pairs of opposite edges have matching directions.

For

K

, take

[0, 1] \times [- 1/2, 1/2]

. Identify

(x, - 1/2) ≃ (x, 1/2)

with matching directions, and

(0, y) ≃ (1, - y)

with reversed directions. These equations specify the arrows on the two fundamental-domain drawings.

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