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On page 220 of Peter Engel's Geometric Crystallography, he describes a 38-sided convex polyhedron that can fill space.

I've seen this this accepted as the record in various places, but I've never seen a 3D picture. Has anyone ever managed to make one?

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2 Answers

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Here is the figure (I assume it is this one) in Grünbaum's paper to which Joe Malkevitch refers:
      Fig. 10: Engel

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There is a "schematic drawing" of the Engel polyhedron in Marjorie Senechal's book Crystalline Symmetries. It appears as Figure 1.14 on page 14.

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