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I want to show a gif like this: Menger Sponge Slices

Menger Sponge Slices

I think I can ues a big Cuboid to cut the MengerMesh.

m3=MengerMesh[2,3]
re=Parallelepiped[{5/3,25/3,5/3}+#,{{-(10/3),-(20/3),20/3},{-(20/3),-(10/3),-(20/3)},{20/3,-(20/3),-(10/3)}}]&;
Manipulate[RegionDifference[m3,re[t]],{t,-2.45,-2.4,0.01}]

Oh, that's a really bad idea, a bit slow and don't works under some cases (bug?)...

And careful, sometimes it'll crash the frontend...


And idea for generating such animation?

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    $\begingroup$ Check out Show[m3, ClipPlanes -> InfinitePlane[{{0, 0, 0}, {0, 1, 1}, {1, 1, 2}}] ] $\endgroup$ – Jason B. Dec 29 '17 at 17:49

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