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cut pyramid ABCD into 8 equal and similar pyramids

Source: IV Soros Olympiad 1997-98 Corr. 11.9 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

June 1, 2024
combinatoricsgeometry3D geometrycombinatorial geometrypyramid

Problem Statement

Cut pyramid ABCDABCD into 88 equal and similar pyramids, if:
a) AB=BC=CDAB = BC = CD, ∠ABC=∠BCD=90o\angle ABC =\angle BCD = 90^o, dihedral angle at edge BCBC is right
b) all plane angles at vertex BB are right and AB=BC=BD2AB = BC = BD\sqrt2.
Note. Whether there are other types of triangular pyramids that can be cut into any number similar to the original pyramids (their number is not necessarily 88 and the pyramids are not necessarily equal to each other) is currently unknown
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