The video below, by on Twitter, shows Penrose triangles embedded into something called "nil geometry". Of the six neighbouring pairs of cubes, three of them can have equal z coordinates, but for the remaining three pairs, one cube unavoidably has to have a greater z coordinate than the next.Īs another additional bonus point, although it's not possible to embed the Penrose triangle into normal, flat, Euclidean 3D space, it is possible to embed it into curved three dimensional space. Note that it doesn't quite form the Math.SE logo, since one cube ends up in front of all the rest. Therefore the cubes' centres of mass can't be given consistent z coordinates.Īs an extra bonus point, even if we don't assume that, and instead assume that each cube is as close to the next as it can be (in the z direction) without the surfaces intersecting, the Math.SE logo still can't be made into a consistent 3D shape, as the following animation shows. Instead, each cube is positioned so that some of its sides are coplanar with those of the next cube, and each cube is separated from the next by some distance in the z direction, where z is perpendicular to the plane of the image. However, if we're assuming that the Stack Exchange logo is a subset of the Penrose triangle then we know the cubes aren't arranged like that. If that was the case it would be incorrect, since it's possible to have mutually overlapping arragements of cubes, as in this image provided by Misha Lavrov. In reply to some of the comments, just to be explicit, the point here isn't just that the cubes all overlap each other.
There's no consistent "z ordering" that you can give to the different parts of the figure, and that's one way to see that it's impossible. You can go around the hexagon in the original logo, in clockwise order, and see that each cube appears to be located further from the 'camera' than the next one in the cycle - which means that each cube is in front of itself. But in fact, each cube is partially obscured by at least one other cube, in such a way that it appears to be some distance behind it. Now note that the cubes are overlapping, so some must be in front of others. Let's add some more cubes to the logo to make it clear that it's a subset of the Penrose triangle (or would be, if it was a real 3D object)
Situated within Charvitha Meadows, a gated villa community at Burugupally in Siddipet, the 3D-printed temple is a three-part structure being built in an area of 3,800 square feet by city-based Apsuja Infratech.Īpsuja Infratech has tied up with Simpliforge Creations, a 3D-printed construction company, for the (function() ) I can't resist posting an answer based on the Mathematics Stack Exchange logo. HYDERABAD: The world's first 3D-printed Hindu temple is being built in Telangana. Now, lotus will prove again to the world the edge that 3D printing will offer to the construction industry when it comes to free-form structures," Gandhi added. "But we have already proved with our Ganesha temple that shapes that are almost impossible to attain with conventional techniques can be done easily using 3D technology. "We are hoping that what we learned from the 'modak' will let us finish the 'lotus' earlier than that," said Gandhi. "With the Shivalay and the modak completed, phase II comprising the Lotus and the tall spires (gopurams) are underway," Jeedipalli added.ĭespite being a challenge, the dome-shaped modak, which required the team to get innovative, took the team only about six hours to print it over a span of 10 days, Gandhi said. The team is now working on the lotus-shaped temple dedicated to Goddess Parvati. After undergoing load testing and evaluation for functional use, it is now being used as a pedestrian bridge in the garden around the temple," said Dhruv Gandhi, CEO of Simpliforge Creations. The concept and design were developed and evaluated by Prof K V L Subramaniam and his research group from the civil engineering department of IIT Hyderabad.
"This was also assembled on-site at Charvitha Meadows, Siddipet. Incidentally in March, Simpliforge Creations had together with the Indian Institute of Technology, Hyderabad built India's first prototype bridge in a little under two hours.
"The three sanctums, or garb has, within the structure represent a 'modak', dedicated to Lord Ganesha a Shivalay, a square abode devoted to Lord Shankar and a Lotus-shaped home for Goddess Parvati," said Hari Krishna Jeedipalli, MD, Apsuja Infratech.
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