The foundation of the trinagon system is symmetry.

Symmetry is too big a word to explore here.

It is found in nature, in mathematics, in 'chaos' and what we perceive as 'order', to name a few.

it is a principle that can give us insights into complex mechanics or processes, be they of the real (material, physical) or virtual (philosophical, social, mathematical ..) kind, without having to understand the exact workings of these.

And really just like that, we can enjoy symmetry. We can derive hypercomplex theories about them, or we can just ..

.. PLAY !

This is the game to give you that opportunity !

Trinagon is a permutation puzzle system.

Not just one puzzle, but many many puzzles that can be played on multiple playgrounds with miriad configurations / layouts / designs / patterns.

Symmetry has many many expressions :) Here you see another one.

(The Dodecahedron game on the left will be available after the 'Hexagon Base' Edition has sold enough to cover further game developement. It is especially interesting for those, who already played the 2x2 rubiks cube to exhaustion), and literally wish for a 'new twist' of the same complexity.

Trinagon puzzles are mathematically (and otherwise) an uncharted area !

( .. because its new :) )

For the rubiks cube many solving systems have been created. Simulations were run and a lot of thinking & processing power got spent on figuring out the rubiks cubes 'Gods Number', and many mathematical papers have been written on this one single puzzle (one resource here ..), and other permutation puzzles.

There are many apps that will autosolve it for you, and there a numerous tutorials where you can learn to apply solving patterns for the rubiks cube.

**Trinagon, being completely new, has not even begun to be explored !**!

If you are a mathematician specialized in group theory (that being the mathematical branch for a permutatiuon puzzle like trinagon or the rubiks cube) or becoming a mathematician, trinagon should hopefully give you a few hours ?, weeks ? months or years of work.

Apart from the simple beauty of the maths involved, maybe the matematically inclined can help with something else.

We would definitely be interested in finding two (or three) algorithms :

- One that can check whether a proposed solution pattern can actually be achieved in play, without the actual solution needed.
- One algorithm, to calculate the least number of moves needed to solve a puzzle !? (Gods Number).

Then small number of moves needed, to solve puzzles has been a surprise to thier own creators already often enough.
- and well maybe therefore .. how about an algorithm that can solve any trinagon puzzle ?

Maybe even do it better than a good player ?

If funds can be generated selling this game, they will be available for research purposes. Feel free to contact us in case this is your line of work/pleasure.

Other mathematically interesting features within trinagon may hopefully be a source of inspiration for many students (of all grades) :

For example :

- platonic bodies (and other polyhedra) and many of their properties.

Even just visual representations, getting a feel for it and learning to 'see' 3D, will greatly improve the ability to analyze and understand polyhedra.
- general symetries in physics and mathematics,
- vector calculus
- probability theory.

Just to make up a few :

- How many different solution patterns (only the end positions) are there to a given colors-only puzzle ?

How does this change when you add facemarkers, and directions ?

- ... and can all of them be achieved / reached in normal play ? (mostly no).

How many can be ? (That's where it gets difficult)

- Why are there exactly 6 rotationtypes ?

Or could there be more ?

- How many turns does it take to move a triangle from A to B, and how many shortest paths are there, depending on the playgound ?

- In the Icosahedron. Do 2 triangles that are as far away as they can be from each other have the same orientation ? Why (not) ?

Is there a connection to how many moves it takes to move from A to B ?

- Is there a useful relationship between the distance of two triangles and the number of moves to bring one to the others place, or exchange them (in the hexagon) ?

- And one out of the game :

In the tetrahedron puzzle. Use one flip-rotator (4,5 or 6) and 3 flat rotators.

Is it possible have only one triangle face flipped ?

Yes / No & Why ? :)

.. Are you sure :) ? I thought i was !

- ... make up your own. There are enough questions for all and for everyone.

After playing a while, a few good guesses might already answer some of these questions or give you an idea of how the get there.

If you have come up with questions and maybe even followed through with some answers, you can sent them to us (for the resource center) or publish them in the forum.

Trinagon first entered it's creators (my) imagination in 1988 or thereabouts.

At that time turbo pascal was the programming language we learned in school. There where none of those cool tools that make programming a breeze nowadays, but the base game could already run with VGA graphics (Anyone remember - 16 Colors at 640x480px).

There were no animations programmed whatsoever. Instead the colors where interchanged. The game could be played using the keyboard. It really was more of a programming excercise, but i thought the concept was pretty cool and well.... New.

The design was exactly like the base layout for the editor, 6 Rainbow colors around the hexagon grid with 9 triangles each.

I played the game about 10 times.

Then i decided, it was to easy to solve, and therefore sort of ... boring :/

No further designs were tried or variations, and the idea discarded as too simple.

Unfortunately the code (even though i do not have a turbo pascal compiler anymore) was not preserved throughout the years.

..

..

Many many years later, in 2015 seeing some puzzle games around, and maybe playing 'monument valley' and other 3dimensional puzzles, the old idea came back in a very different shape :

The same puzzle logic of adjacent interchangeable triangles, but wrapped around symetrical bodies (platonic ones especially).

A very short search led to a wonderful program & learning tool : Geogebra, which allows for 3 dimensional vector calculations and graphical representations and is very easy to learn and apply. (The above picture was made using Geogebra)

With geogebra the basic 3D shapes could be understood and visualized, but it also became clear that the game idea would not necessarily make sense, and really the idea did not seem sooo great, as to make the effort of learning how to program it in nowadays programming environment.

A short dabble into the unity editor made it clear that programming has become a very different kind of animal since 1988. Somehow much easier, with bigger concepts and structures in play that come out of the box, yet at the same time with a rather steep learning curve (unless you wanted to write Yet Another Monster Game).

This year (2018) finally there seemed to be enough time and interest to learn something new. Unity and c#, and some blender modelling started a process that did turn out to be much more interesting than anticipated.

The intention was really just the learning exercise, and the knowledge that, looking at the stupidity of some games out there, even an easy game can be an improvement. (Since then i have learned that it's not soooo easy after all).

Not even 2 months later the game was already playable, but just like its original still lacked something, until ..

the animations in 3D revealed a whole new world of possibilities !

When triangles were allowed to have two distinguishable sides (faces), and then also a direction, things got interesting indeed.

Suddenly a rather simple game evolved into a complex and diverse creation of many possibilities. Who would have thought of that !

To discover this world was and is a pleasure and it's a decent amount of work to develop the details. The process is still going on. The mathematics (group theory) on that example will be a pleasure to see, as will be the creation of many puzzles, and solving them and getting a better idea of the principles.

The actual idea from 2015, wrapping a 2D game over 3D bodies, is still under construction, but already all the foundations are laid, and updates and upgrades already working but not yet publishable. There are many many details yet to finish off, but i do hope that the outcome will be worth the effort.

We don't know, what we don't know.

There are some really cool answers.

But do we have the right questions ?

Very very deep down somewhere in the inner workings of our being, we have assimilated the relationship between cause and effect as being one where cause comes before effect. Pretty much by definition.

Just the same, sometimes later we see our life as questions that need answering. Work that needs to be done. There is first the task and then the effort.

Let there be a question ! Give me an answer.

Clearly this makes perfect sense :)

But !

Where is the FUN IN THAT !

Sometimes beautiful circumstances come together, where we have answers, and only long after we find questions to use them for !

Sometimes the right ideas will find new problems, that they already have solved.

Trinagon was one such case, even in its creation, and it can be a place for this process to continue.

When playing you will realise sooner or later, that intuitively you will have answers to questions you did not even know where there to ask.

Questions may present themselves, for the answers you already have.

Trinagon can be played at any age, unless you're kept too busy in kindergarden, or too busy getting through school chores, you will learn to think in a way that does give you insights into questions that you never knew you could have.

Which ones will those be ? Let them surprise you, surprise yourself with the answers, surprise your friends, and enjoy the game.

Games are never chores. Lets keep it that way.