Cylindrical Cuts (Posted on 2009-01-22)

An object resembling that in the graphic, is carved from a cube of soft material such that its elevations, as seen from the top, front and side, are all that of the drawing at the top. Note that each curve is a segment of a quadrant circle centred on the opposite corner and having the radius of the side of the square. While the object may look like a stellated octahedron, each curved stellated extension is actually formed by six surfaces being parts of cylindrical forms (thus there are 48 actual surfaces which form the object). What percentage of the cube is wasted to create this object? "Impossible" Solid's Volume was a somewhat related problem.

	Submitted by brianjn
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I never did have a solution for this, as such I am pleased to see two different approaches to this. I commend the respective work of both Charlie and Brian Smith. to the reader.

	Subject	Author	Date
	Exact Surface Area	Brian Smith	2009-02-12 13:10:23
	Exact Solution	Brian Smith	2009-01-23 16:13:00
	A Solution I never had?	brianjn	2009-01-22 22:52:15
	re: numerical integration -- note on programming language	Charlie	2009-01-22 16:44:36
	numerical integration	Charlie	2009-01-22 16:35:01