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'Octa-flower' printed from http://nrich.maths.org/
Start with a thought experiment in which you take some regular
octahedra and, on each one, colour two faces that meet at a vertex
but not along an edge. Now imagine taking two octahedra and gluing
them together with coloured faces in contact so that the vertices
where the coloured faces meet coincide. Now glue another octahedron
on, coloured face to coloured face, so that the three vertices
where the coloured faces meet coincide. Continue in the same way as
long as possible. Calculate how many octahedra can be joined
together in this way.