Torus and Klein bottle tessellations with a single tile of pied de poule (Houndstooth)

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Abstract

We design a 3D surface made by continuous deformation applied to a single tile. The contour edges are aligned according to the network topology of a Pied-de-poule tessellation. In a classical tessellation, each edge is aligned with a matching edge of a neighbouring tile, but here the single tile acts as a neighbouring tile too. The continuous deformation mapping the Pied-de-poule tile to the 3D surface preserves the staircase nature of the contour edges of the tile. It is a diffeomorphism. The 3D surface thus appears as a torus with gaps where the sides of the tile meet. Next we present another surface, also a single Pied-de-poule tile, but with different tessellation type, a Klein bottle. Both surfaces are 3D printed as innovative art works, connecting topological manifolds and the famous fashion pattern.
Original languageEnglish
Title of host publicationProceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture
EditorsEve Torrence, Bruce Torrence, Carlo Séquin, Kristóf Fenyvesi
Place of PublicationStockholm
PublisherTessellations Publishing
Pages115
Number of pages122
ISBN (Print)978-1-938664-27-4
Publication statusPublished - 29 Jul 2018
EventBRIDGES 2018: Mathematics, Art, Music, Architecture, Education, Culture - The National Museum of Science and Technology (Tekniska museet) , Stockholm, Sweden, Sweden
Duration: 25 Jul 201829 Jul 2018

Conference

ConferenceBRIDGES 2018
Abbreviated titleBidges
CountrySweden
CityStockholm, Sweden
Period25/07/1829/07/18

Keywords

  • Tessellations, Manifolds, Textile Pattern

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