## puzzle playgrounds

#### The Small & Big Hexagon  :

The Hexagons are the basic training playgrounds to understand the principles of permuting the triangles on surfaces.

They only use an even symetry (6) and are 2D. That makes the distance between two spots on the playground obvious.

The small hexagon is more about symetry and elegant permutations, whereas the big hexagon gives you the 'bigger picture' :) and simpler but efficient sorting of triangles as a task.

Small Hexagon :
Puzzle Type Name : HexS
Rotators : 7
Symetry : 6
Triangles : 24

Big Hexagon :
Puzzle Type Name : HexB
Rotators : 19
Symetry : 6
Triangles : 54

#### Tetrahedron

The Tetrahedron is the smallest platonic solid.
Look these up online :)

Trinagon uses 3 of those & other polyhedra that can be made of (more or less) equilateral triangles.

The tetrahedron is a rather difficult playground as soon as you play with directions & faces, because every move affects 3 out of 4 triangles.

Here you learn 3D on the smallest scale.

Puzzle Type Name : Tetra
Rotators : 4
Symetry : 3
Triangles : 4

#### Octahedron

The Octahedron is the third platonic solid.

Its even symetry makes the puzzles easier than the tetrahedron or icosahedron, but the body is still small enough to make thinking around the corner clearly a necessity.

Every move still affects half of the whole, and you may be finding it difficult to get triangles out of the way to permute just those you want.

Puzzle Type Name : Octa
Rotators : 6
Symetry : 4
Triangles : 6

The Octahedron strongly resembles the 2x2 rubiks cube, which directionally permutes its corners. In case of using rotation type 1 uniformly and 8 colors the matematics should pretty much be identical.

#### Icosahedron

The Icosahedron is the fourth platonic solid.
(The third is the cube - see Rhombic Dodecahedron)

Here you can dive into bigger and all over complex 3D puzzles of a decent size.
With its rotational symetry of 5 it will give you some challenges when using directions and faces.

Puzzle Type Name : Ico
Rotators : 12
Symetry : 5
Triangles : 20

Thie playground already has a 'Board', i.e. an underlying but deactivated body which the triangles could sit on. It's an excavated dodecahedron or 'great dodecahedron'. In a future update all the convex shapes will get a board / inner body.

#### Rhombic Dodecahedron

The Rhombic Doedcahedron has a trinagon history already.

Its apparent shape has outgrown its name, but we still decided to keep the latter.
Its first design was indeed a rhombic dodecahedron, where the rhombes had two triangles on them.
A small change in the distances of 6 Rotators changed the shape, so that every spot is equilateral, and the triangles fit neatly.

A look at the inner rotators reveals that this shape would therefore better be deyscribed as a stellated cube (hexahedron) !
I.e a cube with pyramids on each face.

You may work out the mathematical details yourself :)

This shape has even rotation-symetry, which makes it the second of the even 3D shapes.
This becomes important when solving face & directional puzzles.

Puzzle Type Name : Rodo
Rotators : 14
Symetry : 6 and 4
Triangles : 24 (like the Stellated Octahedron)

Ad 'even shape' :
A playground with even rotationsymetries restricts the possible directions / faces any triangle can have on the whole playground.
More on this will be found on the trinagon homepage in time :)

#### Doubled Tetrahedron

A tetrahedron where edge is divided in two makes the properties of the terahedron mix with those of a nhexagon.

You also gain some interesting 3D symetries around the edges, as you'll quickly experience in the first few puzzles.

This shape is a nice balance between simplicity and compexity, which makes it rather beautiful.

Puzzle Type Name : DiTetra
Rotators : 10
Symetry : 3 & 6
Triangles : 24

PS : Can you see the octahedron made by the inner rotators ?
Sure you can !

#### Tetra Penta Bowl

This a a rather peculiar and irregular shape !
Let it surprise you.

Imagine cutting off part of an icosahedron, and into the resulting bowl you inset a pyramid.

The icosahedron had a symetry of 5. (That's where the 'penta' comes from in the name)
This odd symetry is changed into an even one (6) and the oddity (3) is moved into the center. i.e on the tetrahedron in the middle

The tetra-pentahedron is set to be played from the inside !

Puzzle Type Name : TetraPenta
Rotators : 4
Symetry : 6 & 3
Triangles : 12

#### Pentagon Bi-Pyramid

A simple pentagon with a pyramid on either side.

In its small size, and the strange mix of a small even and bigger odd symetry results in some rather difficult puzzles.

Puzzle Type Name : PentaPyr
Rotators : 7
Symetry : 4 & 5
Triangles : 10

#### 'Football'   as in 'Square antiprism pyramid'  :

Its other name lost in favour of Football, in dedication to my son.

As you play you'll find that it's easier to keep track of the 3 - dimensionality on a shape that has a clear orientation.

The Football offers a well-rounded mix :) of symetries.

Puzzle Type Name : Football
Rotators : 10
Symetry : 4 & 5
Triangles : 19

#### Tria Tria Prism  alias Tri-Augmented Triangular Prism.

As the name indicates it's a triangular prism, with three pyramids.

I'm sure you see why it was shortened to 'TriaTria'.

Another 5 & 4 Symetry here on a smallish shape.

Puzzle Type Name : TriaTria
Rotators : 9
Symetry : 5 & 4
Triangles : 14

PS :
Maybe an idea for two other shapes to be made come up as you read the above ?
All in due time !

#### Stellated Octahedron

The stellated octahedron will give you pause.

It looks complicated, but is nothing more than a few pyramids on a regular octahedron.
The pause will come when you try to bend your brain around the 8 triangles which each of the rotators of the inscribed octahedron permute.

So far it's the only playground with a rotation-symetry of 8.

Puzzle Type Name : StellaOcta
Rotators : 14
Symetry : 3 & 8 !
Triangles : 24

As you can see, the stellated octahedron can be made with two tetrahedrons fused in opposition. Therefore it has 4 extra rotators on the doubled tetrahedron.

#### Truncated Tetrahedron

A tetrahedron where the tips have been cut off.

There is enough space for some simpler puzzles with a twist. Uncomplicated as it is, it still has a few eye openers in store.

Puzzle Type Name : TruncTetra
Rotators : 16
Symetry : 5 & 6
Triangles : 28

#### Penta Prism Pyramids alias stellated pentagonal prism

A pentagon extended into a prism with pyramids on each square face.

Here only two rotators have an odd symetry. All the others are 4 & 6.

There is ample space to move, which would make it a good training playground.
The task often is to not fall into rogue play but still find elegant solutions.

Puzzle Type Name : PentaPrismPyr
Rotators : 17
Symetry : 6, 4 and 5
Triangles : 30

#### Tripled Tetrahedron

So many things to make from a tetrahedron !

This shape is a big as it gets, but offers a nice playground for sometimes partial use or big looong puzzles, with a clear orientation.

You could play the small hexagon puzzles on this one, because of its flat symetry (6) on every surface, and if you think about it, overlapping those on each will lead to some really really hard puzzles.
Watch out for updates of advanced puzzles.

Puzzle Type Name : TriTetra
Rotators : 20
Symetry : 6 & 3
Triangles : 36

...... AND MORE TO COME .....