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Publication Date


First Advisor

Joseph O'Rourke

Document Type

Honors Project

Degree Name

Bachelor of Arts


Computer Science


Polyhedra, Computational geometry, Polyhedra-Models, Geometry-Data processing, Isometrics (Mathematics)


Motivated by physicists wrapping oil drops in ultrathin plastic sheets, we are inter ested in volume-increasing deformations of polyhedra. We implement a constructive proof by Igor Pak in Mathematica. We take as input a tetrahedron and output a submetric deformation that has greater volume. This implies that there is an isom etry that also increases volume. We extend the algorithm to work on any “simple” polyhedron: one all of whose vertices have degree 3. We investigate the relationship between volume and surface area for several of these deformations and discuss our findings.


2018 Syed Zainab Aqdas Rizvi. Access limited to the Smith College community and other researchers while on campus. Smith College community members also may access from off-campus using a Smith College log-in. Other off-campus researchers may request a copy through Interlibrary Loan for personal use.




48 pages : chiefly color illustrations. Includes bibliographical references (pages 47-48)