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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)

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Hints/Tips Possible solution | Comment 2 of 25 |

Here is an idea:

Take a solid sphere (e.g. ball of playdough), and two thin wooden sticks (e.g. skewers). Imagine 3 orthogonal planes bisecting the sphere alined along a traditional x,y,z axis (the z axis looks like a point from the front view). These planes divide the ball into eight sections. Now select a point in the very center of the closest upper right sector (equidistant from the three "corners"). Insert a skewer through that point through the center of the sphere and out the other side.

Let it extend beyond the far side until it looks like it just touches the 2-d circle as viewed from the front. Also cut of the near side to achieve the same optical effect (just touching the outer circle).  You will now see a circle with a slash across it from each view.

Next, with another skewer, do the same thing from the front upper left section to the rear lower right. Again make sure the skewer extends beyond the sphere just enough to appear to touch the edge of the circle when viewed from straight on.

Finally, one more skewer from the upper right rear sector throught the center to the lower left front. This one will overlap with the first on the front view, but is necessary for the other  views.

In the end, you have a ball of dough, with three 6 sharp points sticking out of it, so don't throw it at anyone.

If I can come up with a decent drawing of this, I'll post it.

  Posted by SteveH on 2004-10-23 17:45:22
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