A Note on Objects Built From Bricks without Corners

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We report a small advance on a question raised by Robertson, Schweitzer, and Wagon in [RSW02]. They constructed a genus-13 polyhedron built from bricks without corners, and asked whether every genus-0 such polyhedron must have a corner. A brick is a parallelopiped, and a corner is a brick of degree three or less in the brick graph. We describe a genus-3 polyhedron built from bricks with no corner, narrowing the genus gap.
5 pages, 3 figures

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Computational Geometry, Discrete Mathematics, F.2.2,G.2

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https://dspace.dare.co.zw/handle/123456789/42906

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arXiv

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