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cover plane with specific non convex pentagons

Source: 2005 Oral Moscow Geometry Olympiad grades 10-11 p3

October 21, 2020
combinatorial geometrygeometrypentagon

Problem Statement

ABCBEABCBE is a regular pentagon. Point B′B' is symmetric to point BB wrt line ACAC (see figure). Is it possible to pave the plane with pentagons equal to AB′CBEAB'CBE?
(S. Markelov) https://cdn.artofproblemsolving.com/attachments/9/2/cbb5756517e85e56c4a931e761a6b4da8fe547.png
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