Cross section of a solid and a plane
A few weeks ago , we saw how a cube can be sliced such that the cross-section is a regular hexagon.
Now, consider a solid obtained from a cube in the following manner: we divide it into 27 smaller cubes like the Rubik's Cube and remove those cubes in the center of faces and the one in the center of the original cube.
This solid is then sliced such that the cut edge is a regular hexagon.
What is the shape of the hole in this hexagon?
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The solid is one step of creating the Menger Sponge fractal. I have made step three on a 3d printer with this very slice. Here is a picture from the rendering software. So you can see the 6-pointed star from the center hole plus six smaller ones and even 42 tiny ones!