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Barycentric subdivision of a tetrahedron

The barycentric subdivision of a tetrahedron has f-vector

(f_{0}, f_{1}, f_{2}, f_{3}) = (15, 50, 60, 24) .

Its two-skeleton therefore has Euler characteristic

15 - 50 + 60 = 25

and homology

H_{0} ≅ Z

,

H_{1} = 0

, and

H_{2} ≅ Z^{24}

.

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Solution