Guy Inchbald shared something interesting with me. The Weaire-Phelan foam is a relaxation of a packing of irregular dodecahedra and tetrakaidecahedra. Dissect the dodecahedra into pentagon-based pyramids by adding a vertex at the center, then glue their bases to the surrounding tetrakaidecahedra. Amazingly the faces line up and the result is a decahedron that tiles space by itself. I made the video below.

Guy's page about Weaire-Phelan: https://steelpillow.com/polyhedra/wp/wp.html

#Math #Geometry #Tiling

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Inspired by the parquet deformations made by @csk and @panlepan, here is a tour through six space-filling polyhedra: cubes, Weaire-Phelan, body-centered cubic, the Laves graph, face-centered cubic, diamond cubic.

In the lower-left is the unit cell with 8 cell centers shown as spheres. We run Voronoi on every frame to make the animation.

Code: https://github.com/timhutton/voronoi-honeycombs
Video: https://www.youtube.com/watch?v=OlRSXm6Pt9k

Craig's G4G talk: https://www.youtube.com/watch?v=T9zyvvXZmc8
Vincent's Geogebra page: https://www.geogebra.org/m/dyf5phvB

#Geometry #Tiling #Tessellation

I’m an author, illustrator and designer interested in #origami, #MathArt, #tiling, education and other things that I’ve found here like like #Enshittification and #genuary. I use graphics software and programming environments including #geogebra. #introduction
Most media is by me unless otherwise stated.

Detail of a fountain at the Hassan II Mosque, Casablanca, Morocco

#TilingTuesday #geometry #tiling #MathArt #photography #design #IslamicPattern #IslamicArt #zellij #zellige #TravelPhotography

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Fractal kite tiling

#Tiling #Fractal #Geometry #MathArt #MathsArt #Art

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