Titlebook: Reshaping Convex Polyhedra; Joseph O‘Rourke,Costin Vîlcu Book 2024 The Editor(s) (if applicable) and The Author(s), under exclusive licens

培养

Anecdote

978-3-031-47513-9The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

一小块

构想

Domes and Pyramids tailoring. A key step (Lemma .) repeatedly slices off shapes we call g-domes. Each g-dome slice can itself be achieved by slicing off pyramids, i.e., by suitable vertex truncations. Lemma . will show that slicing off a pyramid can be achieved by tailoring, and thus leading to Theorem ..

FLINT

Pyramid Seal Graph skipped and visited later. The chapter explores a topic that emerged from our approach of tailoring via sculpting: roughly, the distribution of “traces” or “scars” left on the resulting polyhedron . by the digon-tailoring process. We called them “seals” in the previous chapter. The . is the graph on . formed by all seals.

nascent

Tailoring via Flattenings slightly weaker than tailoring via sculpting, either with digons (Theorem .) or with crests (Theorem .), weaker in the sense that the resulting scaled copy of . could be arbitrarily small. Nevertheless, the proof and algorithm have the advantage of operating entirely intrinsically: the 3D structure of . and . is never invoked.

critique

序曲

Vertices on Quasigeodesicsx polyhedron . has a quasigeodesic . containing at most one vertex, then the vertex-merging described in that theorem leads to an unfolding of . to a cylinder . and then to a non-overlapping unfolding, an anycut-net for ..

eustachian-tube

讽刺滑稽戏剧

alls durchschnittlich minderbegabt sich zeigten. Und zwar betrug die Abweichung im Durchschnitt etwa ein Drittel von der der Eltern. Zwischen den. Durchschnittsnoten der Großeltern und Enkel zeigte sich eine Übereinstimmung von nur wenig geringerer Größe.