So, as you all know, Erworld's magic system is incredibly fascinating, with all eight possible intersections of three elements that then interact with three different axes for 24 total magic disciplines. The chart that Parson drew in his eye-book is undeniably helpful in understanding how they're related, but I thought I'd try another method. And then I wanted to improve it, and accidentally created something cool enough to share.

First, I made a Venn Diagram. Three overlapping circles representing Life, Motion, and Matter, such that each class has a spot for its particular intersection with three, two, one, or none of these elements:

I made this awhile ago, but didn't really like the spacing issues, where Clevermancy is implied as everything else and the inner spots are so crowded I had to leave Retconjuration out to make everything fit, so I didn't think it was worth sharing.

So recently I looked it over again and tried triangles, hexagons, and finally chevrons(or whatever you choose to call 2/3 of a hexagon), finally coming up with a design I liked, for several reasons I've included in this next image:

Which is a decent two-dimensional representation, enough for it's own full image:

image

However, it reminded me of another set of triangles, an eight-sided die, and I was able to work out a slightly adjusted overlapping, now with different colors that could combine:

image

This better idea distracted me from making the 2-D shuriken shape large enough to fill in all the classes and disciplines, which may eventually be a thing, but I like the end result with all it's information:

image

And finally, here's the die template by itself so you can print out as many eight-sided Erfworld magic dice as you want:

image

I only had tape but I printed out a test subject and it worked fairly well. I personally use the triangles to roll for a discipline, using whatever triangle is pointed toward me on the top face(Moneymancy in this case):

I still don't like having to shorten the names of the disciplines, but at this point it's a 3D-modeling project which I don't have the skills or program to really make this what it could be. Here's the baton, have fun. :)

 

UPDATE:

...or not, I decided to keep the baton and run another lap. I'm not saying someone can't model a better one, but I kept working on the things I didn't know how to do until I've been able to put together a model that approximates what I think this idea could become. I have no idea if it's printable(and some of my downloading file attempts made it look like it might not be), but here's what I've made:

And the lighter side:

I've also added some "hole" panels on each side to get rid of the little protrusions of each triangle at the vertices, but left them off of the above panels so you can see the engraved text. The actual model looks like this:

The whole model can be seen or adjusted at: https://www.tinkercad.com/things/jGDP3iIydoI 

Also, I forgot to add the table I modified to keep track of colors:

Also also, I added the text to each triangle as etched text while they were all flat, and saved a copy of that(which was a good thing because it took me four or five tries to get them put together right). This might be easier to read, and is available here: https://www.tinkercad.com/things/gVYisp9GTiQ 

This one might be used for a better arrangement, or just to print out and assemble this nicer version(on paper is what I meant, but 3D printing is theoretically also possible, it'll just be a while before I can test that).

 

(NOTE: User was awarded 75 shmuckers for this post.)

 

UPDATE #2 (August 24): 

A superb comment by onigame prompted a rework of the arrangement of disciplines within each class so that when arranged in three dimensions the Erf, Fate, and Numbers disciplines each align as an axis passing through the die. I'd gotten stuck with the 2D pattern I made and tried to preserve that across the models, but this works out so much cooler for the 3D end result.

I redid the flat version first, rotating each class triangle so that the green Erf triangles aligned with how they needed to be folded, then switching the others as needed(resulting in some different text spacing, since I did "Numbers" different to make it larger). This one is useful to print out on paper, and the new organization neatly telegraphs the folding, since the colors go together:

Next, I reworked the 3D model the same way, which was much easier than folding the new flat model:

Finally, I realized that this new arrangement allowed for 24 triangle pieces(each made of a square and two "hole" pieces to cut it down to the right shape, and therefore in modeling terms 72 pieces) to be replaced by only 6 pyramid pieces, and as a bonus remove the pesky overlap of triangles of different colors:

I'm not perfectly happy with this one, since my alignment was off just a tad in places, enough that I needed to extend the etching "holes" to make sure they reached the surface at all points, but this has the potential to be much easier to rebuild from scratch, and even as it stands should be easier to print, with viewing and files available at https://www.tinkercad.com/things/2ou4B8DdMdI

Thank you all for being such a receptive and insightful community!

Comments

    • HighJumper

      Now that, onigame, is thinking with portals in three dimensions! Seriously, you've improved this idea so much: it looks better, it relates better to the source material, it's even better for modeling! Thank you!

      I've added a few new pictures of the suggested changes and something new I could do because of them, and now I'm going to message Imrahil to see if he'll try printing this one, since it looks more printable on my end.

      • onigame

        That's nice, but why are the axes inconsistent across the faces?  Instead, you can make all the little triangles that meet at the same vertex the same axis. 

        If you imagine placing the octahedron inside a cube, with the vertices at the center of the cube faces, you can then correspond the Erf/Fate/Numbers axes with the X/Y/Z axes.  Then they really would be axes.

        • HighJumper

          Thank you all for commenting!

          @darkalter2000 I would be ecstatic if one of my ideas made it into canon, in whatever form! As I said it was due to space constraints, but since I couldn't get them all in I figured it would be the cheekiest to leave off. ;)

          ThisIsNotDan I considered that, but liked the verb forms for that version. It was a stage in development, though, so I don't feel any real impulse to go back and fix a version that I've improved on. 

          Malady The paper fortune teller idea is awesome, thanks. I like the idea of four of them, one to decide between classes and three for deciding between the eight disciplines in each axis(for instance, picking a random Fate discipline). Also, I'm glad you caught the title pun. :)

          OpusFocus I like the idea, but there's eight classes, not just six, so I'm not sure your model is complete. I'm also not sure what you mean by rotation or order of elements. Maybe the classes with two elements(like Eyemancy with Motion and Life) might include casters that focus on one over the other, but how would the ones with only one(like Spookism with only Motion) be in a different order?

          Fla_Panther I have no idea what you're saying but I would like to. :/ I'll have to check out that video and maybe the playlist(now that I can see the link, it seems to switch between a link and a faulty attempt at embedding).

          Aion Thanks for the printing ideas and tips. I am suddenly remembering a fanfic where everyone suddenly got caster powers and got to select their discipline from a diagram that appeared in front of them. Was that yours? I can't see it on your profile. Jillian got few options but Ansom somehow had tons. I'd forgotten about it, but I think that fanfic was a key inspiration for the original Venn Diagram I made, although I've taken it in other directions since. Anyone know this fanfic?

          Update: I found the fanfic by Count_to_10 that got this whole idea rolling a couple years ago. The particular inciting sentence was in Part 5, Ch 23: "There was also a diagram of interlocking circles that represented the eight classes of magic, with the Erf, Fate, and Numbers subclasses accessible for each." My ideas have gone away from that particular diagram, but I imagined that as something like this, although much nicer with each section as a button:

          Pax Yes, I described why Retconjuration was missing in the text below that image. I put it in everything else.

          Imrahil I'm thrilled to hear you tested it, but I don't know enough of 3D modeling or printing to know how those extra bits are showing up or how to fix it. I saw that weirdness on most of the downloads I tried, too. :/

          zbeeblebrox I thought about clarifying I was using pigment vs light primary colors. :/ By the shortened one, do you mean the last image or the third image, the symmetrical shuriken?

          • zbeeblebrox

            Oh right, the other primary colors! I was really confused at first because I assumed you meant red, green and blue.

            But the design is really clever. I actually like the shortened one a lot, it's very clean

            • Imrahil

              I downloaded the STL file and loaded it up in my slicer (I do have a 3D printer) but am having some issues with the .STL.  It seems there are weird extra polygons 'floating' around the model and the slicing program tries to path them for printing.  The face for Stuffamancy is also missing the 'inscription,' appearing as a blank triangle.  Just fyi.   =)

              • Malady

                OH! ... This is a "Diegram"!

                Not a "diagram", but a Die-gram! A.k.a the singular of dice! ... Nice!

                • Pax

                  Based on the Venn Diagram ... there's an entire discipline of magic that's missing ... !

                  Every single zone has three disciplines, except one: Matter/Motion, which has only two: Croakamancy (Fate) and Shockamancy (Erf).

                  That says, to me, that there must be another entire discipline of magic, one that is Matter/Motion (Numbers).

                  • Aion

                    Late to the party, but just wow! First, your Venn circles are exactly how I "up-modelled" the magic system in my own mind based on Parson's notes. Secondly, simply phenomenal isomorphic transforms! Have a chunk-o-shmuckers!

                    Third, regarding rendering challenges for your polyhedra, there are several options you might want to consider (if you haven't already):

                    • Outsource to a commercial SLA or SLS print shop, such as Shapeways
                    • Use a glue-up approach with an FDM/FFF printer, where you print individual sides, or "side assemblies", then glue them up. IMO, this is a must for success when attempting fine text with FDM, but YMMV by printer. That variable mileage is why I don't actually recommend FDM for this application, though; SLA or SLS are much more preferable.
                    • Use an SLS or DLP resin printer. While this  would probably produce an acceptable 3-D "solid" mesh render, printing individual sides and then gluing them up would also be perfectly acceptable with this method too. Text resolution should then be excellent right down to the X-Y res of the printer, which for resin can be thousands of DPI regardless of the light source.

                    Keep up the fantastic work-- and the fantastic lateral thinking!

                    • Fla_Panther

                      OP, if you understand the math, great, if not that's okay too. But hopefully you can follow the multiplication rules for the diagram drawn in

                      - the triangle with a circle in the middle. The important thing to note is that what appear to be straight lines going through the triangle are not. They represent a three-dimensional circle or loop that you are looking at from the side. Technically, it's a three-dimensional representation of a four-dimensional object the professor is using to help explain eight-dimensional (Octonion) math. (FWIW, this is apparently some ground-breaking theoretical stuff that does a really good job of explaining in a very simple way stuff that mathematicians and physicists have had a hard time explaining until now.)

                      I highly suggest watching the whole set of videos in that playlist. I don't even fully understand the math either, but I get enough of it to see some really cool shit in there, and I think it helps make some sense of Erfworld's multiple axes too.

                      • OpusFocus

                        Inspiring work. That third image reminded me of 6 mangatiles

                        Magnatiles

                        Which got me thinking about what rotating these tiles would mean.

                        If we pretend the order of Life (Red), Motion (Blue) and Matter (Pink) makes a difference, you could make an 'orthogonal magic system for a parallel Erf. 

                        Parallel Erf Magic

                        • Malady

                          With all this paper stuff... My mind latched onto the idea of a "Paper Fortune Teller", a.k.a Cootie-catcher.

                          Usual designs only allow 8 results, so that could only select Classses, or one of the other 3 sets of 8.

                          • ThisIsNotDan

                            This is awesome! In the one where you shorten the names, I notice "Retconjure" is still too big for its britches. You might try shortening that to just "retcon."

                            • Ildriss

                              This is fantastic! Thank you very much for sharing :)

                              • darkalter2000

                                I like the Magic Venn Diagram. The diagram honestly seems like something Parson might at some point have in his notebook as a visual shorthand to replace his old table. Before you said retconjuration was cut off I simply thought you were leaving it off cheekily. The whole thing seems like something the author should consider stealing off you.

                                Edit: Of course with different line textures and symbols so it can be black and white.

                                 

                                • HighJumper

                                  Sorry about the small image sizes, they should be bigger now.

                                  • WurmD

                                    Share the high res versions, so we can print :)

                                    • Bandaid

                                      That looks like:
                                      1. A lot of work.
                                      2. Really cool.