A New Pyramid-Like Shape Always Lands the Same Side Up
https://www.quantamagazine.org/a-new-pyramid-like-shape-always-lands-the-same-side-up-20250625
* tetrahedron: simplest Platonic solid
* mathematicians made one that’s stable only on one side
* confirms decades-old conjecture
https://en.wikipedia.org/wiki/Platonic_solid
#math #polyhedra #tetrahedron #balance #JohnConway #PlatonicSolids
I tried to model these origami as transformation between cube and octahedron in Geogebra, but ended up with this instead
#MathArt #geometry #animation #loop #geogebra #tetrahedron #3d
@mrdk @unnick Maybe looks better with the cube visible?
#MathArt #geometry #animation #loop #geogebra #cube #tetrahedron #3d
@mrdk @unnick I'm kind of surprised and not surprised about how the tetrahedron turned out.
#MathArt #geometry #animation #loop #geogebra #tetrahedron #3d
Today, I learned that some football clubs are using Reuleaux tetrahedrons instead of spherical balls in training to improve goalkeepers' reflexes. https://en.wikipedia.org/wiki/Reuleaux_tetrahedron
Video source: https://x.com/futebol_info/status/1899217444235043025
#Football #FootballClub #FootballClubs #Club #Clubs #Spherical #Reuleaux #Tetrahedrons #Tetrahedron #Ball #Balls #Geometry #Sport #Sports #Soccer #Goalkeeper #Reflex #Reflexes #Training #InterestingPost #Pustam #Raut #Math #Maths #CR7 #LM10 #LeoMessi #LionelMessi #CristianoRonaldo #Ronaldo #FootballTraining #ReflexBall #Messi
Looking to print a painter’s pyramid? These tetrahedrons stand out with geometries fully optimized for flawless 3D printing. Available in 15 heights, from 2 cm to 12 cm (~0.5”–5”).
Find all the details and download here: https://www.printables.com/model/631687
Fluorescence
By Liz West
#granarysquare #kingscross
#art #artwork #uv #uvlights #installation #installationart #lizwest #artist #colour #colours #tetrahedron #festive #pyramid #London #londonphotography #artphotography #Fluorescence #fluorescent #light #lightphotography #christmas #christmastree #neon
Corriere.it - Homepage by di redazione LOGIN
Una piramide che «vola» sull'acqua e pesa fino a 75 tonnellate: ecco il superyacht «Tetrahedron»
Progettato ma mai costruito, è una piramide volante in fibra di carbonio e acciaio. Ogni lato dovrebbe misurare 21 metri e potrebbe viaggiare fino a 71 chilometri orari
Translated:
A pyramid that "flies" on water and weighs up to 75 tons: this is the superyacht "Tetrahedron".
Designed but never built, it is a flying pyramid made of carbon fiber and steel. Each side would measure 21 meters and could travel up to 71 kilometers per hour.
#Tetrahedron
https://www.corriere.it/tecnologia/cards/il-superyacht-tetrahedron-la-piramide-volante-che-vola-sull-acqua/la-piramide-dei-mari_principale.shtml
How come we don’t have a less clumsy word for the regular #tetrahedron? 🤔
It’s the simplest of the Platonic solids & is such a symmetric polyhedron. 😍
I mean, we have “pyramid” and “prism” for its siblings, but I’ve only found “triangular pyramid” as a synonym for it. 😒
(1/2) 3D Seed of Life
What you're seeing here is the "seed" for an ongoing study involving the Seed of Life, Flower of Life, and 64-tetrahedron grid. Even at its early stages with the 3D Seed of Life, I am gaining new perspectives and insight into this sacred form. The 3D software even allows you to view the shape from the inside as it spins around you and through you. There are so many life-like shapes that emerge by tilting and turning the Seed of Life in various ways, adding and removing spheres, adjusting transparency, etc. I am definitely seeing this in a whole new way!
One of my main curiosities at this stage has been volume ratios. There are already some unexpected findings. Despite the irrational nature of pi involved in all of the calculations, one result features the ratio 1.599996 (octave-reduced), which, as you can see, is extremely close to 1.6 or 8:5.
#sacredgeometry #seedoflife #floweroflife #knowledge #knowledgeispower #geometry #tetrahedron #vesicapisces
One day, one decomposition
A051677: Tetrahedron-tree numbers: a(n)=sum(b(m),m=1..n), b(m)=1, 1,3, 1,3,6, 1,3,6,10,..., 1,2,...,i*(i+1)2
3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/Tetrahedron-tree_numbers.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/Tetrahedron-tree_numbers.html
#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #numbers #tetrahedron #tree #graph #threejs #webGL
An here, another loop with the 3d-printed painter's tetrahedrons. 😆
Finally managed to snap some shots of various test prints of the painter's tetrahedron.
https://www.printables.com/model/631687
Oddly enough, my camera can't quite grasp the neon-orange hue of the 80mm version—it's as if the color is too vibrant for the sensor.
The #pentachoron or #pen, also commonly called the #5_̶cell or #4_̶simplex, is the simplest possible non-degenerate polychoron. The full-symmetry version has 5 regular tetrahedra as cells, joining 3 to an edge and 4 to a vertex, and is one of the 6 convex regular polychora. It is the 4-dimensional simplex. In addition, it can also be considered to be the regular-faced pyramid of the #tetrahedron, or the pyramid product of a triangle and a dyad. This makes it the simplest segmentochoron as well, and it is designated #K_̶4.1 in Richard Klitzing's list of convex segmentochora. It is also the 5-2 step prism and gyrochoron. In geometry, the #5_̶cell is the convex 4-polytope with the Schläfli symbol {3,3,3}. It is a 5-vertex 4-dimensional object bounded by five tetrahedral cells. It is also known as a #C5, #pentachoron, #pentatope, #pentahedroid, or #tetrahedral_pyramid. Again, it is the 4-simplex (Coxeter's α 4 {\displaystyle \alpha _{4}} polytope), the simplest possible convex 4-polytope, and is analogous to #the_tetrahedron in three dimensions and #the_triangle in two dimensions. The #5_̶cell is a 4-dimensional pyramid with a tetrahedral base and four tetrahedral sides.The regular #5_̶cell is bounded by five regular tetrahedra, and is one of the six regular convex 4-polytopes (the four-dimensional analogues of the Platonic solids). A regular #5_̶cell can be constructed from a regular tetrahedron by adding a fifth vertex one edge length distant from all the vertices of the tetrahedron. This cannot be done in 3-dimensional space. The regular #5_̶cell is a solution to the problem “Make 10 equilateral triangles, all of the same size, using 10 matchsticks, where each side of every triangle is exactly one matchstick, and none of the triangles and match sticks intersect one another” (again: no solution for this exists in three dimensions).
@Apotheiite
The #tetractys, when we advance its dimensional complexity from 0 to 3, ends in the #tetrahedron. When we advance it once more (pictured in following tweet) to get the 4th dimension, we have the #pentachoron.
