Newsgroups: sci.math, rec.puzzles
Followup-To: sci.math
From: hoey@zogwarg.etl.army.mil (Dan Hoey)
Date: 10 Jul 91 22:00:30 GMT
Subject: Boxes with same volume and area

The pool puzzle I answered a few months back led me to consider the
problem of boxes (rectangular prisms) with integer sides and the same
volume and surface area.  There are a lot of them, such as the 3x8x8
and the 4x4x12 with common volume 192 and area 224. There are even
triples, such as the 144x14x12, 112x24x9, and 63x48x8 with volume
24192 and area 7824.

Is there a set of four or more such boxes?
Are there bounds on the ratios of the sides?
On the ratio of area^3 to volume^2?
Can you give a formula to generate the solutions?

Is there anything published on this problem?

Dan Hoey
Hoey@AIC.NRL.Navy.Mil