Mathemagical Box--A Mind Experiment

[Turtle]

___Not a bad description at all Fish. Is it clear what I want you to count yet? We certainly have elements from symmetry here & one such is that if you ink up the box & roll it along like a log, you create what is called a 'frieze' pattern. The box is capable of 3 unique frieze patterns.

[Tormod]

Looks like an Escherian fish pattern to me.

[Buffy]

"Escherian fish pattern" == "Tesselation" for those of you who were wondering....

Metamorphose,
Buffy

[Fishteacher73]

Would it be safe to assume that each side w/ the same dimensions has the "same" pattern (although they appear hand made and there are more than likely subtle difference, in essence they are equivilent)? I.e. each large side has the same design and each smaller end has the same design?

So you could have a B(bottom), Si(side), B (bottom). ---Fliping it end over end l __ l ?
Every B would have to be followed by a S. At each flip you could flip it N,S, E,W. Each Si flip could then be followed by a E/W Si or a N/S B? (Or inverted, depending on how you started).

Does that make any sense?...I am trying to verbally describe possible visual patterns...Not the easiest.

[Turtle]

Not easy at all; you ask the right questions however. In fact, every "side" is different & the carving began at the opening & I worked out in a spiral. I ignored the edges as boundries & wrapped the pattern right over them.
You also have it right to name the "sides" & now since you see we have 6 different such "sides", I have these names for them.
Face 1 or F1 is the large "side" with the opening you see in the photo
Side 2 or S2 is the long thin "side" you see in the photo
End 1 or E1 is the top smallest "side" you see in the photo
Face 2 or F2 is the other large "side" which is in back & not seen in the photo
Side 1 or S1 is the long thin "side" you can't see in the photo
End 2 or E2 is small "side" the box is sitting on(which of course you can't see in the photo)

The name of the print in the picture is thus F1S2E1F2S1E2.
Last for this post, the carving technique is called 'chip carving' & more specifically I used what is called a '6 cut chip'. I proceded by laying out 1 'chip' & then carving it, laying out another chip next to it & carving it, & so on round the box. 6 years of off & on carving to completely cover the box with carving.

[mother engine]

is there another hole in it? is it pictured in the position in which you would use it?

i would sit and stare at it until an application came to mind and then put it away for fear of the possible consequences of said use.

a unique murder weapon? some kind of oriental training exersise? hardcore shower sponge? i have it: to provoke interesting questions from people online.

[Turtle]

Q:is there another hole in it?
A: No
Q: is it pictured in the position in which you would use it?
A: Only in the vein of your comment: "i would sit and stare at it until an application came to mind and then put it away for fear of the possible consequences of said use."
Q:a unique murder weapon?
A: Indeed
Q:some kind of oriental training exersise?
Aossibly
Q: hardcore shower sponge?
A:No:excess water may cause the glue to fail
Q: i have it: to provoke interesting questions from people online.
A: it is now.

[Turtle]

___The way I think I can count the total possible prints is to construct a tree graph & simply count directly. I have only printed 20 different prints & I still don't know for sure how many more are possible.

___After making a few prints though, I realized each print actually counts as two, because you get the same result printing the order of 'sides' backwards. Also, I found something unexpected & that is some prints terminate after five 'sides'; this is because the last unprinted side does not end up adjacent to the 5th printed.
___I hope this clarifies this inky issue enough to prompt some solutions from you. I also have another use for the box I have not revealed. The magic continues.

[Tormod]

Is the number of prints important to understand this thing?

[Turtle]

(Grinning ear to ear) No, not really. If you see that one of the uses is making prints, that's enough. The math is as you know my constant obsession. I give you this hint Tormod; the next 'mystery' use is musical. Any guesses?

This box is extremely in the vein of multifunctionality I brought up in the Lounge.