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math.GT2021
Three-dimensional Rep-tiles
Ryan Blair, Zoe Marley, Ilianna Richards
A 3D rep-tile is a compact 3-manifold in that can be decomposed into finitely many pieces, each of which are similar to , and all of which are congruent to ea…
math.GT2021
Self-replicating 3-manifolds
Ryan Blair, Ricky Lee
In this paper we explore the topological properties of self-replicating, 3-dimensional manifolds, which are modeled by idempotents in the (2+1)-cobordism category. We give a classi…