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An 'Impossible' Solid (Posted on 2004-10-23) Difficulty: 4 of 5
The discipline of Draughting/Drafting usually has exercises requiring the presentation of 3 elevations of an object; aerial or plan view, front view and side or end view. A standard house brick would be 3 rectangles drawn in relation to its dimensions.

I understand that somewhere through the 1930ís a German architect proposed a drawing for a solid object which many deemed impossible, but I have a lovely brass model that invalidates those claims.

The challenge was: Given one drawing that represents all three elevations - Create the object!

Examples: A square is a cube. A circle represents a sphere but a circle crossed with a ' + ' sign might be a beach ball with circles around its 'x,y,z' circumferences; like an orange cut into 8.

NOW, this object in question is represented by a circle crossed by an 'X' or multiplication sign.

MY CHALLENGE is twofold:
1. What does this object look like? Describe as many of its properties as possible.
2. How might you create it as a demonstration in, say, 2 or 3 minutes? I suggest a firm but pliable medium like children's 'playdough' and a tool like a very simple kitchen utensil would reasonably create an approximation of this solid.

See The Solution Submitted by brianjn    
Rating: 3.2000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Finally, I see it. | Comment 17 of 25 |

Sometimes it just takes knowing that it can be done, to do it. Again taking Owl's general approach: this solution is much simpler than what I was trying before. Just take a cylinder of diameter d (perhaps using playdough and a circular cookie cutter). The hight must be at least d. Lay the cylinder on its side and slice down throught the center with the same cookie cutter. Slice one more time (orthoganally to the other two).

Now, by definition we see a circle exterior when viewed from any side. In addition, The edges of the other circles make an "X" pattern from the side.

I've tried to make it with playdough, but unfortunately the stuff squashes when I try the second and third cuts.


  Posted by SteveH on 2004-11-12 17:40:54
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