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There is a 3D object, so that when you look at it from 3 different angles, you can see the shape of a triangle, rectangle, or circle.

What does it look like in 3D?

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    $\begingroup$ Welcome to Puzzling SE! $\endgroup$ – NL628 Mar 5 '18 at 6:56
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I do remember this from a blog from the last month (and from a childhood puzzle book).

3D printed version of object source: http://www.georgehart.com/rp/makerbot/makerbot.html


So this solid has:

A circular base(can be formed out of a solid cylinder by carefully slicing from the centre line of circular symmetry)
A rectangular cross-section when cut through the central line through to the sharp edge.
A triangular cross section when cut at the midpoint of the sharp edge, perpendicular to the edge.

Image:

three shapes explained.

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    $\begingroup$ Just beat me to it! I found a quite nice image online which makes it very clear if anyone still doesn't quite understand $\endgroup$ – Beastly Gerbil Mar 5 '18 at 7:26
  • $\begingroup$ @BeastlyGerbil Nice. Thanks, will add it the answer :) $\endgroup$ – ABcDexter Mar 5 '18 at 7:26
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    $\begingroup$ I worked that shape out in my head. So It must be quite easy to do!! $\endgroup$ – n00dles Mar 5 '18 at 18:28
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    $\begingroup$ I was going to say the shape of a toothpaste tube. $\endgroup$ – Jasen Mar 6 '18 at 5:48
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The classic answer has already been given, but there's another class of possible answers invented by Professor Sugihara of Meiji University, namely his "ambiguous objects" illusions:

enter image description here

enter image description here

It might be possible to add one more viewing angle to include the missing shape to either one of the shapes above.

Images are from this page (contains links to 3D printer models): http://home.mims.meiji.ac.jp/~sugihara/ambiguousc/ambiguouscylindere.html

Professor Sugihara's English language page with many more "impossible objects": http://home.mims.meiji.ac.jp/~sugihara/Welcomee.html

Here's a video where some of his ambiguous objects are rotated in front of a mirror: https://imgur.com/GzE06tt

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    $\begingroup$ Wow! That's really amazing :D $\endgroup$ – ABcDexter Mar 5 '18 at 10:43
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    $\begingroup$ Mind -> blown... $\endgroup$ – n00dles Mar 5 '18 at 18:24
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    $\begingroup$ Oh wait, before I visit the sites, I think I get how it works. Those blocks of perfect geometrical shapes only look that way from where the camera is.(??) I'ma delete this if I'm wrong! $\endgroup$ – n00dles Mar 5 '18 at 18:33
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Hmm a

traffic cone? If you look at it from the side it looks like a triangle, from the top it looks like a circle and from the bottom is looks like a square?

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    $\begingroup$ From the top it kind of looks like a circle inside a square. $\endgroup$ – Bass Mar 5 '18 at 8:14
  • $\begingroup$ In other words as @Bass: You are using two different types for your argument. The one that looks like a cicle from the top, doesn't looke like a square from the bottom. $\endgroup$ – Tom K. Mar 6 '18 at 7:02
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I can imagine something similar to ABcDexter's solution but slightly different.

Imagine a class of cone-like objects that share common basis (a circle) and their tops lay on a line segment paralel to the diameter of the basis (they must also be opposite edges of a rectangle, in other case we can get a parallelogram in result). Lets merge them together, so that a point is contained in a new object when it lays inside any of source objects. My sketch describing the idea:
My sketch describing the idea

Why it is a valid solution:

Each source cone is perceived as the same triangle from a direction paralel to the line section on the top. Each source cone is perceived as a circle from the top.
About the rectangle: common basis form the lower edge. All summits of cones summed together at the line segment form the upper edge. Left and right rectangle edges come from the first of all and the last of all cone sides (they are sections derived from their summits to certain points on the basis)

Why I think my solution is better:

ABcDexter's solution looks like an artificial, human made object with sharp edges, that it is possible to make using lathe and cutter. My solution has got a smooth, continuous surface so we can imagine, that exists a higher probability to find similar object in nature (for instance a rock in a river, a tooth of some animal etc...)

The real solution:

In reality it is a class of objects that share this skeleton: Skeleton of the generalized solution
Mine and ABcDexter's solutions are only some special cases...

Additional notice:

Because mentioned "cones" are not precisely cones from a mathematical point of view, so let make a more precise definition for them:

  • It is a 3 dimensional object that its surface is bounded by a circle at the bottom and continuous set of line segments at the top, so that each line segment starts at the same arbitrarily chosen point above circle (named as the object's summit) and terminates attached to some point at the base circumference.

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    $\begingroup$ Nice answer :) The image provided in my solution were built using a 3D printer. $\endgroup$ – ABcDexter Mar 5 '18 at 15:49
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    $\begingroup$ @ABcDexter Indeed, but I mentioned lathe and cutter because I think it would be very easy to make such object from metals using some machining technology (turning and milling). With mine example it would be a lot harder so casting should be involved. $\endgroup$ – mpasko256 Mar 6 '18 at 15:57

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