1. What 3D objects are represented by a pair of concentric circles in its plan (viewed from above) and a pair of concentric circles for its front elevation (vertical face)?

2. What would a #1 object be if it also has a side elevation that is concentric squares [with corner diagonals]?

For part 1, a sphere, say a bowling ball, would do, if two holes are drilled in it with their axes being perpendicular diameters of the ball, placed so one end of one of the holes is on top and one end of the other hole is in front.

A start toward part two would be to start, not with a sphere, but rather with the intersection of two infinite cylinders, say the volume where x^2+y^2<=6 & y^2+z^2<= 6, and holes drilled along the center axes of the two original cylinders. The third view will then be a square, but the only other lines in that view will be the two diagonals of the square--there will be no internal square.

A square prism could be cut out with its axis viewed lengthwise in this view, but it would interfere with the two circular views, so that is not allowed.

 

Posted by Charlie on 2006-08-02 14:29:52