^ the="" study="" of="" convex="" polyhedra="" in="" ordinary="" space="" is="" a="" central="" piece="" classical="" and="" modern="" geometry="" that="" has="" had="" significant="" impact="" on="" many="" areas="" mathematics="" also="" computer="" science.="" present="" book="" project="" by="" joseph="" o'rourke="" costin="" vîlcu="" brings="" together="" two="" important="" strands="" subject="" --="" combinatorics="" polyhedra, ="" intrinsic="" underlying="" surface.="" this="" leads="" to="" remarkable="" interplay="" concepts="" come="" life="" wide="" range="" very="" attractive="" topics="" concerning="" polyhedra.="" gets="" message="" across="" thetheory="" although="" with="" roots, ="" still="" much="" alive="" today="" continues="" be="" inspiration="" basis="" lot="" current="" research="" activity.="" work="" presented="" manuscript="" interesting="" applications="" discrete="" computational="" geometry, ="" as="" well="" other="" mathematics.="" treated="" detail="" include="" unfolding="" onto="" surfaces, ="" continuous="" flattening="" convexity="" theory="" minimal="" length="" enclosing="" polygons.="" along="" way, ="" open="" problems="" suitable="" for="" graduate="" students="" are="" raised, ="" both="" a
The focus of this monograph is converting--reshaping--one 3D convex polyhedron to another via an operation the authors call "tailoring." A convex polyhedron is a gem-like shape composed of flat facets, the focus of study since Plato and Euclid. The tailoring operation snips off a corner (a "vertex") of a polyhedron and sutures closed the hole. This is akin to Johannes Kepler's "vertex truncation," but differs in that t
