A Note on Objects Built From Bricks without Corners
Mirela Damian, Joseph O'Rourke

TL;DR
This paper presents a new genus-3 brick polyhedron with no corners, advancing the understanding of brick constructions without corners and narrowing the gap from the previously known genus-13 example.
Contribution
It introduces a genus-3 brick polyhedron without corners, providing a significant reduction from the previously known genus-13 example and addressing a question about genus-0 cases.
Findings
Constructed a genus-3 brick polyhedron with no corners
Narrowed the genus gap from 13 to 3
Provided insights into brick polyhedra without corners
Abstract
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.
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Taxonomy
TopicsCellular Automata and Applications · Computational Geometry and Mesh Generation · Architecture and Computational Design
