What is the least area surface that can block all lines of sight through a cube?

geometry/opaque.cube New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

What is the least area surface that can block all lines of sight
through a cube?

>The Opaque Square Problem is still unsolved, and Scott Landrum posted
>the best known solution.  Analogously, there is an Opaque Cube
>Problem: What is the least area surface that can block all lines of
>sight through a cube?

-- David G Radcliffe <radcliff@alpha2.csd.uwm.edu>, "Opaqued Polygons",
   April 1995

Show solution

David G Radcliffe <radcliff@alpha2.csd.uwm.edu> wrote:
>The best known solution an area of approximately 4.2324.  Martin
>Gardner has offered a $50 reward for the best improvement on this
>solution.  See the November 1992 American Math. Monthly for more
>details.

Interesting.  The obvious answer has area 3sqrt(2) ~ 4.2426 .  The
record must be a small variation.

-- Dave Ring <dwr2560@tam2000.tamu.edu>

[ Editor: the problem is unsolved; the collected postings give only
the best known area, about 4.2324 (for a cube of side 1). ]