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PrintChina Girls' Mathematical Olympiad
China geometry
Problem
Determine if there exists a convex polyhedron such that (1) it has 12 edges, 6 faces and 8 vertices; (2) it has 4 faces with each pair of them sharing a common edge of the polyhedron.
Solution
The answer is yes, as shown in the figure.
Final answer
Yes
Techniques
3D ShapesEuler characteristic: V-E+F