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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(2): Maybe Solution | Comment 13 of 25 |
(In reply to re: Maybe Solution by SteveH)

Hi SteveH,

Assuming the discs aren't transparent, are you sure the intersections are not hidden? Given a view, the two "flat" axes are hidden by the "flat" petals, while the diagonal intesections are shared by all three pairs, and are right behind the heads-on edges, yes?

I agree, if there are intersections unhidden, smoothing with tapering should work under the right definitions; good idea! I need to make a model; this hurts my head :-)


  Posted by owl on 2004-10-24 15:47:24
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