Minimum Perimeter Developments of the Platonic Solids
A development of a convex polyhedron is a connected plane figure obtained by cutting the surface of the polyhedron and unfolding it. In this paper, we determine the length and configuration of a minimum perimeter development for each of the Platonic solids. We show that such developments are obtaine...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | text |
| Published: |
Archīum Ateneo
2011
|
| Subjects: | |
| Online Access: | https://archium.ateneo.edu/mathematics-faculty-pubs/80 http://thaijmath.in.cmu.ac.th/index.php/thaijmath/article/view/70 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Ateneo De Manila University |
| Summary: | A development of a convex polyhedron is a connected plane figure obtained by cutting the surface of the polyhedron and unfolding it. In this paper, we determine the length and configuration of a minimum perimeter development for each of the Platonic solids. We show that such developments are obtained by cutting the surface of the polyhedron along a Steiner minimal tree. We introduce the concept of Steiner isomorphism to develop a search algorithm for determining these Steiner minimal trees. Each of these trees is completely symmetric with respect to rotation around a fixed point. |
|---|