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Diary: Kelvin’s Piecepack Pyramid Dimensions

Posted by kelvSYC on 8-26-2013

Almost as soon as I finished writing that last diary post, I really looked into the dimensions of my prospective piecepack pyramids, and whether I can get them 3D-printed.  First, I want to investigate the dimensions.

The reference document dictates that the side of a piecepack pyramid form an isosceles triangle with a 36-degree angle at the tip of the pyramid for all sizes.  As stated, the base of the pyramid range from 1/2″ (A) to 27/32″ (F), in roughly 1/16″ increments.  (Pyramid F is slightly larger).  My highly imprecise measurement method also reveals that the distance from the tip of the pyramid to a corner range from 13/16″ (A) to 1 3/8″ (F), in increments of roughly 0.3cm.  Doing some math, the heights of these pyramids would be 0.73 inches (A) to 1.24 inches (F), with Pyramid E (at 1.13 inches) being “pawn-height” (a pawn is 1 1/8″ in height).

With a pyramid base increasing by 1/16″ from one size to the next, it would leave me with a thickness of 1/32″ for the pyramids (and allow the other 1/32″ for some “play”, similar to Looney Pyramids specs).  The problem here is that 1/32″ is a tad too thin for most 3D printers that deal with plastic (a quick look at materials used in 3D printing reveals that most plastics require a thickness of 1mm; 1/32″ is roughly three quarters of that).  If you are willing to print using metal and drive up your materials cost, it’s worth a shot though. But it’s likely to be cheaper to just cut sheet metal to make pyramids if you’re going that route…  So, for the budget conscious (for the definition of “budget-conscious” that goes out of their way to make pyramids out of plastic, that is), it looks like 1/16″ is the smallest thickness that I can realistically use.

A 1/16″ thick pyramid would need 3/32″ difference between pyramid sizes if we were to go by the above.  If we were to keep pyramid F at 27/32″, then pyramid A would have 3/8″ base.  In other words, something slightly larger than a zero-pip Looney Pyramid (a Looney pawn is known as a “one-pip” pyramid, drone “two pips”, and queen “three pips”, their bases and heights form a natural arithmetic progression, so a “zero-pip pyramid”, created in practice by hacking off the tips of other pyramids, is a natural progression in reverse).  If that’s too small and you would like to keep pyramid A at the half-inch square base, then pyramid F would be 31/32″ square – still permissible within the constraint that the base of pyramid F must be no larger than a quarter of a piecepack tile (ie. one inch square), and slightly smaller than a Looney queen.

Can I possibly make things even thicker for good measure? Possibly.  If we had 3/32″ thick pyramids (ie. 1/8″ difference in base sizes), then pyramid A can have a 3/8″ square base and pyramid F can have a 1″ square base.  All fairly good base sizes, and as 3/32″ is roughly 2.4mm, you could work with a wider choice of materials, I suppose.  But 1/8″ thick bases is definitely out.  I would imagine that a pyramid with a 1/8″ base (the base of A if E was 3/4″, like it is with the reference document) would be very difficult to handle.

So, now for the heights of said pyramids.  The problem is that, the thicker we make our pyramids, the less likely that they will, in fact, stack neatly (that is, pyramid A should be completely obscured by pyramid B if you were to place it on top of pyramid A).  While I haven’t tried out maintaining the specified heights and seeing if this occurs, I had been considering adopting the Looney Pyramid model of having a fixed height to base ratio.  Specifically, Looney Pyramids maintains a 7:4 height-to-base ratio (up to 1/32″ of an inch), and if I were to take pyramid E to be “pawn height”, then a base of 7/8″ (used in the 3/32″ model and the 1/16″ model with the larger pyramids) would give these pyramids a height-to-base ratio of 9:7.  Now a 9:7 ratio, rounded to the nearest 1/32 of an inch, almost exactly gives a height difference of 1/8″ between pyramid sizes. (Pyramid A, at 9/14″, would actually be closer to 21/32″ than 5/8″, but the heights for B, C, and D would fall between a nice eighth-inch multiple and the next 1/64″ larger, and for F the 1/64″ smaller)  That seems a bit convenient, let’s see if this actually stacks…

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Diary: Kelvin’s Quest for a Piecepack

Posted by kelvSYC on 8-25-2013

It’s been a long time since I’ve made an entry in the Collection.  I’m so incredibly behind on the Guide that it’s becoming a running joke, and, well, my game collection has become that much larger that I’ve rarely been playing Settlers anyways.  (I’ll get back to the Guide, just you wait…)

So a bit about myself.  When the Guide first started, I was a student in Canada with a lot of time on their hands (for a good chunk of it, I compiled the Guide without a copy of Settlers at my side).  In the last 13 months, I’ve called Seattle my new home, and with that (and the consolidation of my game collection between different locations) and the fact that “I’m only here to work”, that leaves game playing out of my life for the most part.  Still, from time to time I’ve broken out a few board games to play.

For a while, I was on the print-and-play kick, printing every fan expansion to Dominion and burning through 10 printer cartridges in short order.  It was thanks to a few BGG contributors that I also crossed off one item on my board game wishlist: a homemade piecepack.

For those who don’t know, piecepack (http://www.piecepack.org) is an open source gaming system that can be used to play a bunch of games.  It consists of a number of suits (at least four), each with six tiles, six coins, one six-sided die, and one pawn.  The system highly encourages players to make their own, and their specs are fairly well documented.  A number of companies such as Blue Panther do, in fact make commercial piecepacks available for purchase, made from high-quality laser-cut wood.  Personally, however, I was enamoured by a BGG contributor’s custom piecepack made from plastic, and so I sought to make one for my own.

The BGG poster had mentioned that he had gotten all the parts he needed from a place called TAP Plastics, and there just happened to be one location a short walk away from where I worked.  It wasn’t easy sourcing out all of the parts, but I got from them a bunch of blank tiles (via their custom cut acrylic service), pawns (custom cut acrylic rods), dice (from their cube bins), and coins (again from their parts bins).  Add a few pieces of laminated label paper, and my 12-suited plastic piecepack set was now a reality.

The problem, though, is that a good number of games make reference to an accessory known as “piecepack pyramids”.  A piecepack pyramid set consists of six pyramids per suit, lettered from A-E.  Unlike the piecepack itself, the specs were not fairly well documented, and from what I had searched online, the only pyramids in existence were made from a reference document, meant to be printed on cardstock and assembled.  Though many commercial piecepack publishers (not Blue Panther, though) offered sets of piecepacks with cardstock pyramids (likely made from the reference document), I wanted a plastic set of my own.  There is, however, one major problem: the dimensions of the pyramids simply make this not an easy task.

To demonstrate what I mean, let’s take a close analogue of the piecepack pyramids: the Looney Pyramids.  The piecepack pyramids were made as an open-source alternative to the Looney Pyramids while making it more piecepack-like with its theme of “six”, allegedly over the fact that the Looney Pyramids weren’t (and still isn’t) open source (though at one point homemade Looney Pyramid creation was encouraged, and its specs also well-documented), with some elements even protected under intellectual property legislation (the specifics of which are too complicated to explain here).  The Looney Pyramids consists of three different sizes of pyramids: pawns (small), drones (medium), and queens (large).  According to the specs, the bases of the pawns were 9/16″, the drones 25/32″, and the queens 1″.  This makes the pyramids 3/16″ thick, allowing for the pyramids to stack inside each other.  (Originally, Looney Pyramids, under their original name of Icehouse Pyramids, were solid pyramids; it was not until the “Treehouse era” that the pyramids were made stackable.  In turn, piecepack pyramids were designed based on the stackable pyramids of this era, and the piecepack tiles were specced so that Looney Pyramid queens would take up a quarter of the piecepack tile.)

Taking some measurements of the reference piecepack pyramid dimensions, I notice that the bases increased in size by 1/16″ from one size to the next (with a slight deviation from E to F), from 1/2″ for A to 3/4″ for E.  Pyramid F was slightly larger at 27/32″, but it still meant that piecepack pyramids would have to be extremely thin to have something that resembles the 1/32″ “buffer zone” that the Looney Pyramids enjoy – hence the use of cardstock for pyramids in the first place.  It would also mean that if it were to be made from plastic, the fact that it could literally be as thick as cardstock meant that it would be too brittle to be of use without enlarging the pyramids (there was some wiggle room in the size of pyramid F, since the largest it could be was 1″), or worse, enlarging the tiles (the most expensive component of my custom plastic piecepack, outside of making these pyramids, of course).

So, let’s redesign the piecepack pyramids a bit.  Is it at all possible to create piecepack pyramids that are, say, 1/16″ thick (thick enough that it can be reasonably handled)?  The Looney Pyramids’ pawn is comparable to a piecepack pyramid’s B pyramid (except that it is just under a quarter inch shorter), while the Looney Pyramids’ drone is just a hair larger than the piecepack pyramid’s E pyramid (again, shorter in height).

So far, it looks like I have to do a little math to get some good pyramid sizes going.  Then it’s another matter to find a plastic material that I can make these revised pyramids out of.  I wonder if I can get them 3D-printed…?

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