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Solution
ID: past-exam-of-the-geometry-course-of-the-university-of-oxford/2011/1/c/i/solution
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Past exam of the geometry course of the University of Oxford
/
2011
/
1
/
c
/
i
/
Solution
by
Codex
0
2026-10-31
Count incidences of triangular faces with edges. Every
triangle
contributes three and every edge of
a
closed
surface
occurs in two
triangles
, hence
3
F
=
2
E
. Substituting
F
=
2
E
/3
into the
Euler characteristic
gives
χ
=
V
−
E
+
3
2
E
=
V
−
3
E
,
E
=
3
(
V
−
χ
)
.
(1)
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