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Publication Date

2025-5

First Advisor

Ileana Streinu

Document Type

Honors Project

Degree Name

Bachelor of Arts

Department

Computer Science

Keywords

platonic solids, nets, unfoldings, tiling, tessalation, computational geometry

Abstract

For which platonic solids in dimension d do all of the solid’s nets tile Rd−1, for arbitrary d? For the dodecahedron and icosahedron, we give counterexamples in d = 2, whereas for the octahedron and tetrahedron, we provide them in d = 3. For the cube, the question remains open, although we prove that every cube net in arbitrary dimension is a simple shape. We also suggest several sufficient criteria for determining tilability in d = 2.

Rights

©2025 Heather Robertson. 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.

Language

English

Comments

[6], 52, [2] pages: color illustrations. Includes bibliographical references (pages [59-60]).

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