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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.)
Some Thoughts X marks the spot | Comment 4 of 25 |

The problem gives that:  "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."

And if I understand the problem, all three elevations or drawings should look like:  "a circle crossed by an 'X' or multiplication sign".

At first I thought that a circle crossed by an 'x' would be the same as a circle crossed by a '+'; but it's not.  In the case of the '+' signs, the limbs of each plus sign point to the plus signs in the center of the drawings for the other elevations, ie 2 plus signs on the equator (one at zero longitude, and one at 90 longitude), and one at the north pole.  But an 'x' at zero longitude and zero latitude, doesn't point to the north pole.

SteveH's way may be the answer, but I would think that where the skewers are imbedded in the play-dough, there would not be a line on the drawing.  I think the drawing of the skewers method would show a circle and an incomplete cross where the 2 limbs of the cross don't meet each other in the middle:

       \     /

       /    \            like this with a circle around it.

The problem doesn't state how big the 'x' is relative to the size of the circle.
If you painted 'x's with short limbs in the appropriate places, then this could be the answer; but longer limbs on the 'x' begin to show up in the other elevations.

Summary:  if an imbedded feature, such as a buried skewer, shows up in the drawing, then I think SteveH has the correct answer.  But if not, and if the 'x' can be small, then just paint an 'x', or cut a short 'x' at each appropriate spot.  If not, and if the 'x' has to be large then I have no idea.

I took a 6 cm potato, and speared it 6 times all the way through with a 1 cm wide knife blade making 6 'x's (N pole, S pole, and 4 points along the equator).


  Posted by Larry on 2004-10-23 18:59:35
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