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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 Maybe Solution | Comment 9 of 25 |

It seems that there doesn't have to be unique solution. Notice that the circle with a plus could be gotten by three discs intersecting perpendicularly.

And this idea leads to a possible solution. Take two cards, intersect them perpendicularly, lie them on their side (don't flatten them) and cut them straight down with a sharp biscuit cutter. This is like the previous "plus" example, except the cards are now ellipses so that when view at a 45deg angle, we see a disc. Now take three sets of these cards (a total of 6 cards) and intersect them so that their axes are perpendicular and with each of the three views, one set is seen edge-on as an X.

Make sense? And notice the introduction of a kitchen utensil :-)


  Posted by owl on 2004-10-24 03:52:55
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