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Pendentive Dome Construction

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Level 43 : Master Fish
NOTE: Idk why the images arent working, but you can right click and open them in a new tab, or here is a link to an imgur gallery with all the pictures: imgur.com/a/LWeidsf

So imagine you have a square building and you want to put a spherical dome on top of it. How do you do it in a way that looks cool and doesn’t defy the laws of gravity? Unsurprisingly there are many solutions to this problem, but some may be better than others. In the following image, the light gray concrete square is your building and the dark gray circle is where you want your dome. While the black concrete circle is clearly related to the square, you may not yet see why it is critical.

Pendentive Dome Construction Minecraft Map

Now lets look at what happens when the square becomes a 20 block high wall and the black circle becomes a sphere. At 20 blocks high, a circle drawn around the sphere makes the red concrete line, which you’ll notice is the exact same circle as the original dark gray concrete circle, just 20 blocks higher.

Pendentive Dome Construction Minecraft Map

The next step is to add the dome itself. Simply put, the dome is just a sphere with the same radius as the initial dark gray circle from the first picture, but its center is at the same height where the walls intersect with the sphere generated from the black circle. This makes a dome sitting on top of the building directly related to both the black sphere and the light gray walls. This is shown in the picture below.

Pendentive Dome Construction Minecraft Map

At this point we have all but one of the pieces we need to construct our structurally sound dome. That final piece is the support. So what shape would be good? If you’re screaming TRIANGLES ARE THE SHAPE WITH THE MOST STRUCTURAL INTEGRITY, you’d be right, but in this case we don’t want triangles because our dome is constructed entirely out of radial and rectilinear lines, and a triangle would look out of place. Instead, I’ll pull a trick from Roman classical antiquity and build an arch, which is also and extremely efficient load bearer. These arches should be located at the intersections of the gray walls and black sphere.

So now we have a dome, support, and walls. What’s left? You’ll notice that there is a lot of unnecessary bits of wall and sphere left that are totally negated by the structure we’ve added. These bits are highlighted in the next image in light blue.

All that’s left is removing those extra blue parts. This leaves behind walls, a support system, a dome, and a building made entirely out of similar, related, proportional geometry. The black glass is what’s called a “pendentive.” This is just one of many strategies for bridging the gap between a square building and a circular roof.

This last image is the final product. The light gray blocks are shapes generated from the original light gray square, the black blocks are the ones generated from the original black circle, and the dark gray blocks are generated from the original dark gray circle.

Play around with this idea, and if you make something cool, post a link to it in the comments!
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