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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.)
re: Solution - flaw | Comment 8 of 25 |
(In reply to Solution by Tristan)

After thinking about my solution, I realized that it doesn't quite work out.  Take the front elevation.

  A--B  Sticks CDGH are seen from front,
/| /|  DBHF from side,
C--D |  and ABCD from top.
| E|-F  Stick E is not needed, and neither is D.
|/ |/

Stick C is in front of stick A, but there is an arc inbetween them.  While we can't see A from the front, we can see the arc, and it will be sticking out slightly, along with the arc between H and F.  The result will be a lopsided X, where the upper left and lower right parts are longer.  This might be acceptable, but when considering the side view, the lopsided X will be a reflected, so the elevations do not look the same.

I'm not sure whether this flaw is enough to make the solution invalid though.

  Posted by Tristan on 2004-10-23 22:29:10
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