Rasmus<p>Seems like there are several solutions for the monohedral tile. Some which are of a more hyperbolic nature. (2/n)</p><p><a href="https://mathstodon.xyz/tags/Tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Tiling</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> <a href="https://mathstodon.xyz/tags/3d" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3d</span></a> <a href="https://mathstodon.xyz/tags/3dprinting" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3dprinting</span></a></p>
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#geometry
7 posts · 4 participants · 0 posts today
Rasmus<p>A monohedral hexagonal tiling of a 2-periodic infinite surface. Maybe someone can help me with the right terminology here? As can be seen from the animation using a Maximum Entropy Stress Algorithm (startpoint of animation) to get to a regular embedding of the tiling in \( \mathbb{R}^3 \) only gets you so far. You need to to add more restrictions to get to an embedding where all hexagons are the same. (1/n)</p><p><a href="https://mathstodon.xyz/tags/Tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Tiling</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> <a href="https://mathstodon.xyz/tags/3d" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3d</span></a> <a href="https://mathstodon.xyz/tags/3dprinting" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3dprinting</span></a></p>
Rasmus<p>The hexagonal tile is of course slightly skewed. (2/3) <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>TilingTuesday</span></a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>tiling</span></a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a></p>
Rasmus<p>The tiling can be divided down into different modules of higher genus. One can be seen below. (2/3) <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>TilingTuesday</span></a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>tiling</span></a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a></p>
Rasmus<p>Monohedral Hexagonal Tiling of infinite stacked surface with triangular, hexagonal and rhombic channels. (1/3) <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>TilingTuesday</span></a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>tiling</span></a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a></p>
foldworks<p>Ulugh Beg Observatory Museum, Samarkand, Uzbekistan</p><p><a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>TilingTuesday</span></a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>tiling</span></a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>MathArt</span></a> <a href="https://mathstodon.xyz/tags/photography" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>photography</span></a> <a href="https://mathstodon.xyz/tags/architecture" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>architecture</span></a> <a href="https://mathstodon.xyz/tags/history" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>history</span></a> <a href="https://mathstodon.xyz/tags/design" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>design</span></a></p>
Jean-Baptiste Etienne<p>à partir du pavage sur une boîte de piononos. (<a href="https://es.wikipedia.org/wiki/Pionono" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">es.wikipedia.org/wiki/Pionono</span><span class="invisible"></span></a>)</p><p><a href="https://mathstodon.xyz/tags/geogebra" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geogebra</span></a> <a href="https://mathstodon.xyz/tags/Tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Tiling</span></a> <a href="https://mathstodon.xyz/tags/spain" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>spain</span></a> <a href="https://mathstodon.xyz/tags/scroll" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>scroll</span></a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> <a href="https://mathstodon.xyz/tags/translation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>translation</span></a></p>
foldworks<p>A Geogebra generalisation of Star 8 Octad modular @origami <a href="https://www.geogebra.org/m/mv6gxxbu" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="">geogebra.org/m/mv6gxxbu</span><span class="invisible"></span></a></p><p><a href="https://mathstodon.xyz/tags/animation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>animation</span></a> <a href="https://mathstodon.xyz/tags/loop" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>loop</span></a> <a href="https://mathstodon.xyz/tags/CreativeCoding" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>CreativeCoding</span></a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> <a href="https://mathstodon.xyz/tags/Geogebra" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Geogebra</span></a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>MathArt</span></a> <a href="https://mathstodon.xyz/tags/origami" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>origami</span></a></p>
foldworks<p>Periodic Penrose rhombs, Garden Halls, Marchmont Street, London, England</p><p><a href="https://mathstodon.xyz/tags/FensterFreitag" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FensterFreitag</span></a> <a href="https://mathstodon.xyz/tags/WindowFriday" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>WindowFriday</span></a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>MathArt</span></a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>tiling</span></a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> <a href="https://mathstodon.xyz/tags/photography" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>photography</span></a> <a href="https://mathstodon.xyz/tags/architecture" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>architecture</span></a> <a href="https://mathstodon.xyz/tags/penrose" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>penrose</span></a></p>
Leigh Silvester<p><span class="h-card" translate="no"><a href="https://tech.lgbt/@Natasha_Jay" class="u-url mention" rel="nofollow noopener" target="_blank">@<span>Natasha_Jay</span></a></span> <br>So this has triggered a thought I had decades ago while my partner was watching Star Wars.</p><p>In three dimensional space you wouldn't refer to a Delta Quadrant which is a 2 dimensional term.</p><p>Perhaps there is someone knowledgeable about <a href="https://mastodonapp.uk/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> or <a href="https://mastodonapp.uk/tags/astronomy" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>astronomy</span></a> who knows the term for a quarter of a sphere.....</p><p>Came across the word tetartosphere but assume it isn't in common use.</p>
Geometry + Dynamics Heidelberg<p>The stereographic projection is an old mapping from the sphere to the plane. The image shows a sphere with a distorted pattern on it. Using light the regular pattern is revealed. This is exactly the way the mapping works. The model is available: www.thingiverse.com/thing:5072032<br><a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a></p>
No Starch Press<p>Geometry and topology are reshaping how we think about data. The Shape of Data explores how structure, distance, and dimension impact machine learning—covering networks, manifolds, TDA, and quantum methods. </p><p>Case studies span text, survey, medical, and social data, with accessible math and real code examples in R (Python too). A valuable reference for anyone working in geometric or graph-based ML.</p><p><a href="https://nostarch.com/shapeofdata" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">nostarch.com/shapeofdata</span><span class="invisible"></span></a></p><p><a href="https://mastodon.social/tags/datascience" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>datascience</span></a> <a href="https://mastodon.social/tags/machinelearning" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>machinelearning</span></a> <a href="https://mastodon.social/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> <a href="https://mastodon.social/tags/datavisualization" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>datavisualization</span></a> <a href="https://mastodon.social/tags/rstats" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>rstats</span></a></p>
foldworks<p>Carved stone screen, Agra, India, 19th century, copied from earlier models, Victoria and Albert Museum, London</p><p><a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>TilingTuesday</span></a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>tiling</span></a> <a href="https://mathstodon.xyz/tags/design" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>design</span></a> <a href="https://mathstodon.xyz/tags/MathArt" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>MathArt</span></a> <a href="https://mathstodon.xyz/tags/photography" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>photography</span></a> <a href="https://mathstodon.xyz/tags/architecture" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>architecture</span></a></p>
Rasmus<p>(5/n) <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>TilingTuesday</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a></p>
n-gons<p>A 17x17 rhombus grid for <a href="https://mathstodon.xyz/tags/TilingTuesday" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>TilingTuesday</span></a></p><p><a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> <a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>tiling</span></a> <a href="https://mathstodon.xyz/tags/grid" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>grid</span></a> <a href="https://mathstodon.xyz/tags/squares" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>squares</span></a> <a href="https://mathstodon.xyz/tags/mathart" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathart</span></a></p>
Strum<p>Beach geometry.<br>Brean Sands, Brean Down, Somerset.<br><a href="https://mastodonapp.uk/tags/photography" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>photography</span></a> <a href="https://mastodonapp.uk/tags/beach" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>beach</span></a> <a href="https://mastodonapp.uk/tags/BreanSands" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>BreanSands</span></a> <a href="https://mastodonapp.uk/tags/BreanDown" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>BreanDown</span></a> <a href="https://mastodonapp.uk/tags/groyne" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>groyne</span></a> <a href="https://mastodonapp.uk/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a></p>
Non-Euclidean Dreamer<p>So we saw that in Nilgeometry Geodesics do not generally look straight. Here we have lines parallel to the z-axis, the Seifert-fibers, and they do look straight.</p><p>We are moving around always looking up.</p><p><a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a></p>
Jason Baluyut<p>The angular city.<br><a href="https://ohai.social/tags/photography" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>photography</span></a> <a href="https://ohai.social/tags/urbanphotography" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>urbanphotography</span></a> <a href="https://ohai.social/tags/architecture" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>architecture</span></a> <a href="https://ohai.social/tags/angles" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>angles</span></a> <a href="https://ohai.social/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> <a href="https://ohai.social/tags/nyc" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>nyc</span></a></p>
Sérac<p>Clothoids.<br><a href="https://troet.cafe/tags/Arosa" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Arosa</span></a>, <a href="https://troet.cafe/tags/Graub%C3%BCnden" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Graubünden</span></a> <a href="https://troet.cafe/tags/Switzerland" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Switzerland</span></a> <br><a href="https://troet.cafe/tags/RhB" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>RhB</span></a> <a href="https://troet.cafe/tags/train" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>train</span></a> <a href="https://troet.cafe/tags/track" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>track</span></a> <a href="https://troet.cafe/tags/geometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>geometry</span></a> <a href="https://troet.cafe/tags/rail" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>rail</span></a></p>
mustamakkaraPhoto diary from <a href="https://pixelfed.social/discover/tags/Linz?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#Linz</a>, pt16, <a href="https://pixelfed.social/discover/tags/fensterfreitag?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#fensterfreitag</a> edition<br>
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A window in the local Thalia bookstore, slightly abstracted in post...<br>
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6.6.2025 <a href="https://pixelfed.social/discover/tags/Nikon?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#Nikon</a> z50II | 24mm (aps-c) | f/11 | 1/1000s | ISO2000<br>
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<a href="https://pixelfed.social/discover/tags/architecture?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#architecture</a> <a href="https://pixelfed.social/discover/tags/interiordesign?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#interiordesign</a> <a href="https://pixelfed.social/discover/tags/bookstore?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#bookstore</a> <a href="https://pixelfed.social/discover/tags/window?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#window</a> <a href="https://pixelfed.social/discover/tags/windowfriday?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#windowfriday</a> <a href="https://pixelfed.social/discover/tags/abstraction?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#abstraction</a> <a href="https://pixelfed.social/discover/tags/geometry?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#geometry</a> <a href="https://pixelfed.social/discover/tags/travel?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#travel</a> <a href="https://pixelfed.social/discover/tags/travelphotography?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#travelphotography</a> <a href="https://pixelfed.social/discover/tags/photoart?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#photoart</a> <a href="https://pixelfed.social/discover/tags/austria?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#austria</a> <a href="https://pixelfed.social/discover/tags/oesterreich?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#oesterreich</a> <a href="https://pixelfed.social/discover/tags/urban?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#urban</a> <a href="https://pixelfed.social/discover/tags/urbanphotography?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#urbanphotography</a> <a href="https://pixelfed.social/discover/tags/amateurphotography?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#amateurphotography</a> <a href="https://pixelfed.social/discover/tags/photography?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#photography</a> <a href="https://pixelfed.social/discover/tags/pixelfed?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#pixelfed</a> <a href="https://pixelfed.social/discover/tags/mastoart?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#mastoart</a> <a href="https://pixelfed.social/discover/tags/fediphoto?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#fediphoto</a> <a class="u-url" href="https://pixelfed.social/@photography@a.gup.pe" rel="nofollow noopener" target="_blank">@photography@a.gup.pe</a> <a href="https://pixelfed.social/discover/tags/photodiary?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#photodiary</a> <a href="https://pixelfed.social/discover/tags/dailypicture?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#dailypicture</a> <a href="https://pixelfed.social/discover/tags/dailyphoto?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#dailyphoto</a> <a href="https://pixelfed.social/discover/tags/darktable?src=hash" class="u-url hashtag" rel="nofollow noopener" target="_blank">#darktable</a>
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