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I have here a three dimensional, solid object. Its sides are flat planes. In the following views, all lines are shown — there are no hidden edges.

From the front, this shape looks like:

two concentric squares


From above (at a 90° angle from the previous view), this shape looks like:

two concentric squares


What would this shape look like from the side?

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  • $\begingroup$ Is it all connected, or could it be a cube within a cube? $\endgroup$ Dec 2, 2014 at 12:19
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    $\begingroup$ I'm afraid there may be multiple solutions. The simplest, I think, is an L-shape: two flat squares with a square hole in them connected on one side. $\endgroup$
    – oerkelens
    Dec 2, 2014 at 12:23
  • $\begingroup$ @oerkelens Perhaps I didn't state clearly enough that it's a solid shape; I've edited the question. $\endgroup$
    – SQB
    Dec 4, 2014 at 11:10

4 Answers 4

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Take a large cube. Extract a smaller cube exactly centered in the large cube. You get a hollow cube. Then cut the large cube along a diagonal (i.e. along a plane that contains 2 opposite edges). And put back the small cube.

I don't have the tools right now to produce a correct image. Here is what it looks like from the side.

   ____ /|
  |   /  |
  | /    |
  /      |
 --------'

(Image provided by OP)

A right isoscles triangle, with a smaller traingle of similar shape on it, their hypothenusa aligned, the midpoints of their hypothenusa on the same point, and mirrored on the hypothenuse, so the triangles are 'pointing away' from each other

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    $\begingroup$ You made am assumption that the center square must be elevated, it could be cut off from the surface instead $\endgroup$
    – Ayyash
    Dec 2, 2014 at 15:45
  • $\begingroup$ I know, this is one of multiple solutions. But I didn't want to draw the dotted lines :-). $\endgroup$
    – Florian F
    Dec 2, 2014 at 16:03
  • $\begingroup$ @FlorianF Acutally, I know only of two possible solutions - yours, and its complement, with the smaller cube left out (following your method of construction). Together they form the larger cube you started with. $\endgroup$
    – SQB
    Dec 4, 2014 at 11:12
  • $\begingroup$ There are other solutions with curved surfaces. $\endgroup$
    – Florian F
    Dec 4, 2014 at 12:26
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Could it be a cube missing its middle? Basically, if you drilled a square hole through a cube in all 3 directions, you'd have a cube with square shaped holes.

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  • $\begingroup$ No, because then you'd have hidden edges: the sides of the holes up to the point where they intersect the other holes. $\endgroup$
    – SQB
    Dec 3, 2014 at 11:43
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It will be a plane square. Since there won't be any cavity on the sides.

There are two possibilities for all six sides of the 3D object

Possibility 1

enter image description here

Possibility 2

enter image description here

So, in both cases

the side will be perfect square without any cavity.

Note:From the description and images in the question, it doesn't state that the sides too have cavity, also no info about the dept of the cavity on front and top. So I considered the object with maximum volume.

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  • $\begingroup$ If those smaller squares were cavities, you'd see the sides of them as hidden edges. $\endgroup$
    – SQB
    Dec 3, 2014 at 11:44
  • $\begingroup$ Yes, this is a much better answer. The OP assumed the answer he'she was looking for. This is a much more complete alternative. The shape could be almost anything if the sides are just squares. $\endgroup$ Dec 4, 2014 at 15:29
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My guess is that it is a:

The frame of a cube

Alternatively it might even be:

tesseract projected in 3D (I assume internal edges are not visible).

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