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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 Solution | Comment 5 of 25 |

After playing around with this problem, I found this solution, but I'm not sure whether it will work.  I haven't seen the other comments, but I plan to.

I'm thinking that the x is not something drawn on a sphere, but rather some sticks that stick out of a circle.  To describe the directions of the sticks, imagine that the center of the x is the center of a cube.  There would be 8 sticks going from the center to each of the vertices.  The X seen from each side would be 4 sticks pointing towards you, with another stick behind each stick seen.  Actually, only 7 sticks are needed, because the 8th would just be behind the other sticks from all angles.

To describe the circle, I'll draw a diagram of a cube, each vertex representing the end of a stick.

  A--B  Sticks CDGH are seen from front,
/| /| DBHF from side,
C--D | and ABCD from top.
| E|-F Stick E is not needed.
|/ |/
G--H

I can't just draw a circle, because it needs to look like a circle from 3 sides.  Instead, I'll draw arcs between A and B, B and F, F and H, H and G, G and C, and C and A.  I'm not sure, but I think if you get the arcs just right, it will appear to be a perfect circle from all three elevations.

As for a demonstration, I guess I would bust out some sort of construction set.

Edit: I just realized that stick D is not needed, since from every elevation, there is another stick behind it.  Furthermore, the structure doesn't need sticks at all because they can just be lines drawn on the "circle," or even the edges between different arcs.

Edited on October 23, 2004, 9:04 pm

Edited on October 23, 2004, 9:18 pm

Edited on October 23, 2004, 9:19 pm
  Posted by Tristan on 2004-10-23 21:01:13

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