Samenvatting
We explore ‘pretty’ 3D (skew) polygons and prove their existence. These generalize the well-known regular 2D polygons. In 3D, an additional regularity condition is imposed: all edge torsion angles must be equal in absolute value. The torsion angle of an edge is the dihedral angle between the planes spanned by the edge and each of its two adjacent edges. We define an infinite family of pretty 3D polygons with both rotation and reflection symmetries. This resolves an open problem about the existence of certain pretty 3D polygons. Moreover we present some ad hoc specimens, including two trefoil knots, that do not have reflection symmetry. Finally, we present some pretty 3D polygons that can be morphed while preserving their prettiness.
Originele taal-2 | Engels |
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Titel | Proceedings of Bridges 2021 |
Subtitel | Mathematics, Art, Music, Architecture, Culture |
Redacteuren | David Swart, Frank Farris, Eve Torrence |
Plaats van productie | Phoenix, Arizona, USA |
Uitgeverij | Tessellations Publishing |
Pagina's | 111-118 |
Aantal pagina's | 8 |
ISBN van geprinte versie | 978-1-938664-39-7 |
Status | Gepubliceerd - 5 jul. 2021 |
Evenement | 24th Annual Bridges Conference 2021: Mathematics, Art, Music, Architecture, Culture - Virtual, Helsinki, Finland Duur: 2 aug. 2021 → 3 aug. 2021 Congresnummer: 24 https://www.bridgesmathart.org/b2021/ |
Congres
Congres | 24th Annual Bridges Conference 2021 |
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Verkorte titel | Bridges 2021 |
Land/Regio | Finland |
Stad | Helsinki |
Periode | 2/08/21 → 3/08/21 |
Internet adres |