We first learn of a "strange wooden box" from Friedrich (Muller's first officer) on Happy Happy, Carnage Carnage.

Friedrich tells us:

Muller gave Walter a gold key and sent him
to recover a large amount of gold and a
strange wooden box.

When you ask Friedrich about the box he says:

The box was made of cedar. Muller didn't
tell me what it was supposed to do, or what
it had to do with the gold.

So begins the tale of the Cedar Box.

Muller, true to form, is very evasive about the Cedar Box.

I sent Walter to retrieve something, but it
is a worthless archaeological artifact.
You'd have no interest in it.

Fortunately you spoke to Friedrich first and know that Muller sent Walter to recover a large amount of gold and a box made of cedar.

If you specifically ask about the "box" Muller responds:

People have told you about the cedar box? It
is an art object of great value, but is
otherwise useless.

Ah... so first it is a worthless archaeological artifact and now it is an object of great value... but otherwise useless?

Something does not add up here.

The story of the Cedar Box picks up again when we find Walter on Feel The Power.

Walter tells us:

Muller sent us to get one gold ingot and a wooden
box, he said they were extremely important.
I was leaving though, there was no way I
was going back down to try to find him.

and...

Muller said we needed all twelve ingots, but
that the box would duplicate things which
were placed inside it so we should only get
one. We found the box.

Ah... so the Cedar Box will duplicate things.

So what happened to the box? Walter relates:

The box worked like he said, but the ingots
wouldn't fit inside it. I dropped it when I
was attacked by the invisible demons, it
was useless. But I kept the ingot.

If you are confused about the twelve ingots... then check out the Gold Mystery.

So Walter dropped the Cedar Box when he was attacked by "invisible demons" on the level below.

You'll find it easily enough, there's only one
way to go. There are invisible demons on
the level below this one, watch out. I
escaped them, I ran.

True to his word we find the Cedar Box on the level below... A Plague of Demons.

Initially it was thought that the only thing that the Cedar Box could duplicate was ammo.

However over time people began to experiment with other items.

Back on Feb 8, 1994 Ron Hunsinger posted some helpful advice on comp.sys.mac.games about the Cedar Box and also that it would duplicate not only ammo but also the P4 and the survival knife.

In May 2012 PerseusSpartacus posted a full list of items that could be duplicated by the Cedar Box. He wrote:

• Flashlight: This has some really weird behavior after being duplicated. You can turn on multiple Flashlights at once. However, if you turn on an even number of Flashlights all at the same time, they seem to cancel each-other out; things get darker, as though you didn't have a Flashlight on. On the flip-side, if you turn on an odd number of Flashlights at the same time, the 'brightness level' returns to 'normal' (i.e. it's just like if you had one Flashlight on). Very strange.
• Survival Knife: Been reported before. Didn't test it very thoroughly.
• Walther P4 Pistol: Same as the Survival Knife. Oddly, the Rusted Walther P4 doesn't fit.
• Silver Medal: You don't gain any points or treasure for duplicating this, sadly.
• Ammunition: This should be obvious. Any kind of ammo goes in, the same kind comes out.

Please note that all my testing has been done on a Basilisk II emulator and with PiD v.1.0,
I think. If you find any differences in later versions of PiD or in testing done on a real
Mac OS, please let me know.

Also, screenshots of the Flashlight oddities would help. Just remember to make sure
your inventory is close enough to the World View that we can see how many Flashlights
you have on at the time, and also make sure to include photos of it with both odd and
even numbers of Flashlights on.

Hopper explains this odd flashlight behaviour:

I hadn't tried multiple flashlights before, but it makes sense. There's a separate
player-wide flag that indicates whether your light is on: this is what's actually
used by the engine. Whenever you toggle your flashlight (or rather, *a* flashlight),
the player flag gets toggled too.

Why duplicate a flashlight? Ron Hunsinger put forward the following theory:

Interestingly, the code also tests if the batteries are dead, and won't let you use a
flashlight with dead batteries. Maybe the notion of batteries dying is a leftover concept
from a previous version of the game. That would explain why you can even find additional
flashlights, and why you can duplicate them. As I recall, there's an extra flashlight on
Need a Light, giving the level name a second meaning. You'd have the Cedar Box by then,
and if your original batteries have died when you get there it might occur to you to
try making more batteries.

This is supported by the following line in the Pathways manual (page 18, under Hints):

In case you forget, your flashlight can be turned off. Also, its batteries don't last forever.

Of course, the batteries don't actually run out in the game. Which suggests it was changed late in development.

When looking at the PID data initialization code Ron Hunsinger was able to confirm the items that the Cedar Box could duplicate.

There's a separate table specifically for the Cedar Box that limits it to holding only these items:
Flashlight, Knife, WeaponP4, AmmoP4, AmmoMP, AmmoAKPlain, AmmoAKHE, AmmoAKSabot,
AmmoM16, AmmoColt, Ammo40HE, Ammo40Frag, Ammo40Proj, SilverMedal.

And there it is... the Silver Medal.

Why was this added to the items that the Cedar Box could duplicate?

A simple Bungie joke? The last thing you might think of duplicating.

You cannot duplicate the Silver Medal to increase your treasure score as Ron Hunsinger explains:

I just recently found the list of admissible items in the code (disassembling the v2.0 68K code),
and was excited about being able to duplicate the Silver Medal until I did the math. It takes
1000 Silver Medals to get one treasure bonus point, and your inventory is limited to 256 total
items. You have more important things to clutter your inventory with.

It took me a while, looking at the code, to realize why you don't get extra treasure points
for duplicating it. It turns out that your treasure total is not computed by totaling up what
you're carrying, but as a running total that gets adjusted as you pick up and drop items.
There's no adjustment when you duplicate an item (nor when you eat one, so eating the
Easter Egg shouldn't cost you any treasure points).

However, it appears that dropping all those duplicated Silver Medals could lose you a
bunch of points.

I wonder what would happen if you dropped enough to make your treasure total go negative?
A negative total might look like a HUGE positive total, and you might get a correspondingly
huge treasure bonus. You'd have to drop them in the Labyrinth. No other level can hold that
many dropped items.

***Rats*** It won't work. The treasure total is saved in a signed long, and will simply go
negative without wrapping around at 0.

The Silver Medal of course looks suspiciously like the Iron Cross with a red ribbon.

Only one man in Muller's expedition to the pyramid had the distinction of being awarded the Iron Cross.

Who was he? What was his name? What did he do to be awarded it?

Was he hated by Muller for having something he could never obtain? Think the 1977 movie Cross of Iron (aka Steiner - The Iron Cross).

And how, even in death, did he save your life?

A true hero.