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3

Part of 1993 Bulgaria National Olympiad

Problems(1)

coloring into 2 colours a polyhedral from 2 regular pyramids with bases 7-gon

Source: 1993 Bulgaria NMO, Round 4, p3

7/30/2021
it is given a polyhedral constructed from two regular pyramids with bases heptagons (a polygon with 77 vertices) with common base A1A2A3A4A5A6A7A_1A_2A_3A_4A_5A_6A_7 and vertices respectively the points BB and CC. The edges BAi,CAiBA_i , CA_i (i=1,...,7(i = 1,...,7), diagonals of the common base are painted in blue or red. Prove that there exists three vertices of the polyhedral given which forms a triangle with all sizes in the same color.
geometry3D geometrypyramid