Cut a cube into 5 3D objects with 6 edges each.
Hint:
(I assume there is only one solution): only 4 of the objects are pyramids, ie tetrahedrons with one vertex containing only right angles
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1$\begingroup$ Are you sure there is no error in your question? 4 with 4 edges and 4 as pyramids out of 5 objects implies at least 3 pyramids with 4 edges. Under the usual definitions of which I'm aware there's no such thing. Should this have an enigmatic tag or something? $\endgroup$– Dr XorileAug 28, 2019 at 3:50
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$\begingroup$ Did you mean faces maybe? $\endgroup$– athinAug 28, 2019 at 4:30
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$\begingroup$ @Dr Xorile Yes, as it is presented I have a drawing of this. I may tell you that this is a result (hint?) of unfolding of a certain 4D right angle pyramid and rearranging the components of its "surface" (volume!) $\endgroup$– MotiAug 28, 2019 at 4:36
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$\begingroup$ @athin I meant 5 3D objects. $\endgroup$– MotiAug 28, 2019 at 4:36
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$\begingroup$ @Dr it is clear that you have 4 pyramids - 4 edges implies a pyramid. The additional infor mation of 4 pyramid shows that the 5th object is not a pyramid. $\endgroup$– MotiAug 28, 2019 at 4:40
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1 Answer
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Draw a diagonal line on one of the faces and the orthogonal line on the opposite face. Join the ends of those lines together. With those as the cut points you get four corners of the cube (each with 4 sides) and the remainder is a tetrahedron with 6 edges.
The above is now correct given the update made by the OP.
Here's a rendering of the dissection done in TinkerCad:
This is a link to the Tinkercad object:
https://www.tinkercad.com/things/7cW3ibU52v3
If you go there you should be able to spin it around and stuff.
answered Aug 28, 2019 at 3:40
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$\begingroup$ It is OK. At least you caught it:) I had to be accurate in describing the requirements so a simple cut into 5 slices will not be a solution - this is the purpose of the edges definition. $\endgroup$– MotiAug 28, 2019 at 4:39
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$\begingroup$ The question has been edited to say 6 edges for all objects so I think this solution is valid now. $\endgroup$– hexominoAug 28, 2019 at 8:38
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$\begingroup$ I like the answer, but there was a lot of confusion by OP in the question terminology. Rot13(Jul vfa'g n erthyne grgenurqeba pbafvqrerq gb or n clenzvq?) $\endgroup$ Aug 28, 2019 at 10:03
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1$\begingroup$ @WeatherVane I think that OP is uses the word "pyramid" to refer to a right-angled tetrahedron. This seemed to be the case on a previous question of theirs which I answered. I don't think there exists a 3d shape with 6 edges which is not a tetrahedron. $\endgroup$– hexominoAug 28, 2019 at 11:24
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1$\begingroup$ @hexomino that's true, but a regular tetrahedron is a special case of the pyramid, where any of its faces can be the pyramid's base. $\endgroup$ Aug 28, 2019 at 11:35