Pretty 3D Polygons: Exploration and Proofs

Melissa van Veenendaal, Tom Verhoeff

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

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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-2Engels
TitelProceedings of Bridges 2021
SubtitelMathematics, Art, Music, Architecture, Culture
RedacteurenDavid Swart, Frank Farris, Eve Torrence
Plaats van productiePhoenix, Arizona, USA
UitgeverijTessellations Publishing
Pagina's111-118
Aantal pagina's8
ISBN van geprinte versie978-1-938664-39-7
StatusGepubliceerd - 5 jul. 2021
Evenement24th Annual Bridges Conference 2021: Mathematics, Art, Music, Architecture, Culture - Virtual, Helsinki, Finland
Duur: 2 aug. 20213 aug. 2021
Congresnummer: 24
https://www.bridgesmathart.org/b2021/

Congres

Congres24th Annual Bridges Conference 2021
Verkorte titelBridges 2021
Land/RegioFinland
StadHelsinki
Periode2/08/213/08/21
Internet adres

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