A Trinagon puzzle consists of clearly defined elements :

• Triangles (here 24), equally distributet on the playground in a symmetrical pattern (here hexagonal).
• Rotators (here 7), sitting in the symetry centers of adjacent triangles. They are the spheres / smarties. Here every rotator has 6 triangles. 

The Triangles have a 

• Color ... one out of 10 possible colors

and can also have a

• Face ... up or down, marked with a colored dot.
• Direction ... one corner that is marked with a smaller dot.

The triangles can be moved around unsing the rotators. Each rotator moves its triangles around itself clockwise or counterclockwise, so that they are interchanged (permuted).

It's up to you to find the right moves so that the triangles create the right patterns.

There are 2 basic puzzle setups. One is simply shuffling a pattern and then finding back to the beginning (randomized puzzle), and the other is to go from a beginning pattern to a different solution pattern.

Rotation Types

Trinagon VR is built around a simple idea:
triangles move around rotators.

But the way a triangle changes its orientation during a move can vary.
This is what we call the rotation type.

There are currently 6 rotation types in the game.
Each one describes a different way the triangles behave as they move around a rotator.

If a puzzle uses more than one rotation type, the color of a rotator shows which type it uses.
If all rotators use the same type, the colors are only decorative.

The 6 Rotation Types

Type 1 — Vinyl

The triangles move around the rotator without changing their orientation.

They behave like pieces lying on a vinyl record:
the position changes, but the triangle itself does not turn.

Type 2 — Spin Forward

The tip facing the center is pushed forward in the direction of the move.

After the move, a triangle that pointed toward the center will point forward along the direction of movement.

Type 3 — Spin Backward

The tip facing the center is held back as the triangle moves.

After the move, a triangle that pointed toward the center will point backward, against the direction of movement.

Type 4 — Center Flip

The triangles flip over the axis between them.

The tip pointing toward the center stays pointing inward, but the triangle is flipped to the other side.

Type 5 — Clockwise Conserved

The triangle flips and rotates so that its clockwise-facing tip keeps pointing clockwise after the move.

This is true whether the move itself is made clockwise or counter-clockwise.

In other words:

clockwise is conserved.

Type 6 — Counter-Clockwise Conserved

This is the counterpart to type 5.

The triangle flips and rotates so that its counter-clockwise-facing tip keeps pointing counter-clockwise after the move.

So here:

counter-clockwise is conserved.

Why these 6?

The 6 rotation types currently used in Trinagon VR all follow one important rule:

Every move can be taken back by performing the same move in the opposite direction.

So if a rotator moves clockwise, the matching counter-clockwise move undoes it exactly.

This rule is not immediately obvious, but it is very important.
It means that “moving back” and “undoing” are the same thing.

That gives the puzzle a clean structure:

• moves have clear opposites
• scrambles can be reversed step by step
• the player can understand the system through movement
• the puzzle behaves in a group-like way, where every move has a matching inverse

This is why the current 6 rotation types feel mathematically stable.
They are different, but they all respect the same basic rule of reversibility.

The strange case of types 5 and 6

Types 5 and 6 are special.

If you watch them closely, especially in slow motion, you may notice something unusual:

Type 5 does not look the same when played clockwise and counter-clockwise.
The same is true for type 6.

Most other rotation types look like clean mirrored versions of themselves when the direction is reversed.

But type 5 and type 6 do not.

Why?

Because two things are happening at once:

1. the triangle moves around the rotator
2. the triangle also flips according to a conserved direction

The movement direction changes when you go from clockwise to counter-clockwise.

But in type 5, the conserved direction stays clockwise.
And in type 6, the conserved direction stays counter-clockwise.

So only part of the behaviour reverses.

That is why the animation can look asymmetric.

You may even notice that:

type 5 clockwise visually resembles type 6 counter-clockwise,
and
type 6 clockwise visually resembles type 5 counter-clockwise.

This is not a bug.
It is a consequence of preserving a fixed clockwise or counter-clockwise side while the movement direction changes.

The two possible extra rotation types

Interestingly, there would be room for two more rotation types.

They are not currently used in the game, because they would no longer follow the same simple rule:

the opposite movement direction would not be the undo move.

They would still be reversible.
But the reverse move would be a different type of move, not simply the same move performed backwards.

This means the system would still allow undoing, but:

undoing a move and moving back would no longer be the same action.

Rotation 7 — The natural hook

One possible extra type would be a natural “hook” motion.

The center-facing tip would lift, and the triangle would spin forward into the direction of movement.

So if the triangle moves clockwise, it also spins clockwise.
If it moves counter-clockwise, it also spins counter-clockwise.

The movement and the spin support each other.

This makes the motion feel natural:
the triangle moves and turns in the same direction.

Rotation 8 — The anti-hook

The other possible extra type would be the opposite.

The center-facing tip would still lift, but the triangle would spin backward, against the direction of movement.

So the triangle would travel one way while its spin suggests the opposite force.

This would look much stranger, almost like the motion is fighting itself.

But mathematically, it would be the counterpart to rotation 7.

Rotation 7 would be the natural hook.
Rotation 8 would be the anti-hook needed to undo it.

A more difficult system

These two extra rotation types could create interesting new puzzle behaviour.

But they would belong to a more difficult system.

In the current game, if you want to undo a move, you simply move back.

With rotation types 7 and 8, that would no longer be enough.
A clockwise type-7 move would not be undone by a counter-clockwise type-7 move.

Instead, it would need its corresponding opposite: type 8.

So the puzzle would still be reversible, but the relationship between moves would become more complex.

That is the difference:

The current 6 types are direction-reversible.
The extra 2 types would be reversible, but not direction-reversible.

For now, Trinagon VR uses the clean set of 6.
But the two hidden possibilities remain: a natural hook and its strange reverse.

How to go about solving these puzzles ?

Some basic principles & solving patterns derived from many hours of playtime :

'Rogue Play' below stands for : 

1. 'Rogue Play' (not really a principle) : 
   Solving a puzzle triangle by triangle, without regard for the particular symmetries of the playground or the rotators in play. 
   This is what you'll do when you first try the game, is perfectly fine.
   Naturally this method is clearly not very efficient.
   The fun you have solving trinagon puzzles will grow with your ability to avoid rogue play, and consider more and more of the puzzles properties at the same time.
   
   
2. Backwards exchange : 
   The first pattern. Always used in rogue play. Disregarding other triangles, the goal is to shift the one missing piece into position, by simple
   - moving it out of the way.
   - positioning the space,
   - move the triangle into the space and then turn the positioned triangle to its final position.
   This is similar to solving the first layer of a rubiks cube.
   
   
3. Line Dance : 
   It mostly works out more efficient to keep triangle grouped together. I.e Queuing them up. 
   This may also be misleading (HexS #8 - on the right) and therefore good to know, when NOT to use this pattern. 
   
   
4. Efficient Sorting (or advanced queueing)  :
   Some puzzles seem not much of a challenge, because the pathways to solve them are obvious. They often contain a few steps which could be left out, if the were just done in a different order.
   These Puzzles are often found in the Big Hexagon. What you learn there will help to find the coolest solutions on the smaller puzzles too.
   
   
5. Crankwork fit in :
   Similar to Nr 1 above, but thinking ahead a a few moves in advance, and thereby shifting colors into each other so that 2 queues are built instead of one.
   
   
6. Symmetry patterns :
   Trinagon puzzles are usually highly symmetrical.
   In those cases you can try and divide the board into symmetric partitions and repeat every move of one section in the other(s). 
   This may just bring you to the most elegant solution.
   But : There are many cases where specifically going against symmetry will be necessary !
   Then you need to find out how to best break the symmetry !
   
   
7. Strictly Ballroom : 
   Crankworking  around a symmetry and more than one position synchronously.  In 2D
   A few of the Small Hex Puzzles are especially made to learn this pattern.
   
   
8. Around a corner from both ends (3D crankworks) :
   The small puzzles can really be the most challenging ones. Space is so limited, that every move always includes some triangles which you wish could just stay where they are.
   This is similar to the last moves of the rubiks cube. By the way, the octahedron is really close to a 2x2 rubiks cube in it's properties. So if you can solve the 2x2 rubiks cube you'll be having a much easier time with the octahedron.
   The bigger polyhedra puzzles are a mix between efficient sorting & symetry patterns that go around corners. The first move on one end will have a symetric effect a few moves later when you reach the other side of the polyhedron.
   Combining these basics then often results in surprisingly 'easy' solutions.
   
   These patterns first apply to colors only, but are just as relevant to puzzles containing directions & faces. 

Direction & Face specific ideas to help :

1. Counting distances : (Faces) 
   Counting the distance and the rotationtype moves.
   
   
2. Single odd inversion : 
   Two triangles of a group  on an odd symmetry rotator. Obviously they can never oppose each other, but will always be at least by one closer to each other on one side than the other. An almost- half rotation (e.g  2 out of 5) can sometimes work wonders.
   
   
3. Conservation moves :  
   Prepositioning triangle around a rotator which will conserve their relative orientation,  or break it away on purpose.  Typically needed in rotationtype 5 & 6. 
   Also helps to rule out wrong moves.
   
   
4. Repetitive patterns : 
   .. are a direct application of a quality in permuatation puzzles that can be shown through group theory :
   Repeating a certain move pattern over and over leads, at some point, back to the original state !
   In between there are opportunities that can allow to interchange two or more triangles in a certain way, so that then going on with the move pattern will lead to the desired result.
   This is easy in principle, but not so much so in practice. To find the right exchanges in between often needs actually written down patterns (for mere humans at least).
   For puzzles with difficulties above the 100 this often becomes necessary.
   Just don't let it become work :)
   How this is done : Assume you have triangles of a specific group (mostly meaning : they look the same) which are already in thew right position but turned.
   Find 2 or more patterns that exchanges triangles within the same group. Then write the pattern down, including face & rotation states. From here you'll figure out the rest :)
   
   Btw. this is exactly how the rubiks cube patterns have been found / designed. I.e. Anyone solving the rubik’s cube with a known system is doing just that.