Thank you Julian for your support. I take it as a good sign that you came up with the same Notation in 2008.

I want to put together the "Twisty Puzzle Dodecahedron Notation". We should name it this way and use TPD-Notation as a shortcut for it.
(Konrad's scheme does not do justice to the many contributions from Burgo and others.)

Motivation: When the very interesting mass-produced Face Turning Starminx became available, Andrea felt the need for a commonly used notation for face turning Dodecahedra like Megaminx, Gigaminx, Teraminx, Petaminx, Pyraminx Crystal, FT Starminx, Pentultimate.
The well known Gelatinbrain program uses 12 letters, which are short but not intuitive for a human being.

There is no standard colour scheme for dodecahedra. Not even the twelve colours themselves are standardized. (E.g. my mf8 Gigaminx from Mefferts has very nice coloured stickers but different from the latest mf8 dodecahedra.)
When putting stickers to a dodecahedron, people could try to follow Gelatinbrain as closely as possible or follow the Crazy Megaminx scheme.
Personally I use something close to Gelatinbrain but some sticker colours from mf8 cannot be mapped. E.g. on Gelatinbrain there is no grey. When using colours in a text you should better provide a picture explaining your specific colour scheme. The diagrams below are all made by the usage of the Gelatinbrain program.

Here is the comparison of the Gelatinbrain notation and the result of the discussion above (In the diagrams you see the FT Starminx frontview /backview):



1. Face names

We view the Dodecahedron sitting on a table and one face looking at us which we call F (front).
U (up) is on top and the opposite face on the table is D (down).
R (right) is the visible face at our right hand in the upper part.
L (left) is the visible face at our left hand in the upper part.
B (back) is opposite to F.
For the remaining 6 faces we use two letters:
DR (down right)
DL (down left)
UR (up right)
UL (up left)
BR (back right)
BL (back left)

In the following front view diagram I indicate the invisible faces via arrows.


The B face cannot be shown here.

2. Outer face moves

As in WCA cube notation face letters are used for clockwise turns of outer faces.
U, D, F, B, L, R, DR, DL, UR, UL, BR, BL are single, clockwise turns by 72 degrees of the outer face layer.

The suffix ´ is used for anticlockwise turns:
U´, D´, F´, B´, L´, R´, DR´, DL´, UR´, UL´, BR´, BL´

the suffix 2 is used as a shortcut for two single clockwise turns:
U2, D2, F2, B2, L2, R2, DR2, DL2, UR2, UL2, BR2, BL2

The two suffixes can be combined in two ways(these are synonyms):
U´2, D´2, F´2, B´2, L´2, R´2, DR´2, DL´2, UR´2, UL´2, BR´2, BL´2
or
U2´, D2´, F2´, B2´, L2´, R2´, DR2´, DL2´, UR2´, UL2´, BR2´, BL2´

Note that on a cube U2 and U'2 are identical, but this is NOT true on face turning dodecahedras.
We can write for three single clockwise turns U3, R3 etc. Note that the result for U3 and U'2 is identical.

3. Inner slice moves

We follow the WCA notation for big cubes and use face names in lower case letters denoting an inner slice (inner layer) below an outer face.
u, d, f, b, l, r, dr, dl, ur, ul, br, bl are clockwise turns in the same direction as the respective outer face turns.

This photo shows the turn r halfway completed:


We combine the suffixes ´ and 2 in the same way as above.

For dodecahedra with more layers like the Teraminx we need an additional notation. (This is missing in the WCA notation for big cubes).
We use the prefix `#` and the number of the layer combined with the face name to denote an inner layer turn:
e.g. `#3U` stands for `layer number 3 on the U face`

We allow #2 combined with the face name as synonyms for the lower case letter notation
e.g. #2U is equal to u.

It can be convenient to turn and write two or more adjacent layers together.
In WCA notation 2U is identical to U,u.
Therefore, we allow a number prefix without the # character denoting the number of layers turned together.
To make this a bit clearer we add the character `*`.
E.g. 3*U is identical to U, u, #3U and 3*U is a synonym for 3U (3*U seems better!)

4. Examples for different turns on different Dodecahedra



5. Axis turns of the whole Dodecahedron

We write A(X) for a clockwise turn of the whole puzzle (A = All pieces) around an axis standing vertical on the centre of face X, where X is one of { U, D, F, B, L, R, DR, DL, UR, UL, BR, BL}
Respectivle A'(X) is an anticlockwise turn of the whole Dodecahedron.

y is a synonym for A(U) and y´ for A´(U)

6. Names for single pieces

As the many variants of FT Dodecahedra have various piece types, we cannot generalize the piece names.
Very often a piece can be described by combining face or inner layer names.
Edges can be named using the two faces they are in, corners the three faces they are in.
Because face names have either one or two letters we will use a hyphen to separate the face names e.g. U-UL for an edge or U-R-F for a corner.

For pieces that are only on a single face (one sticker only) we apply the rule that the face name is written first followed by further classification if there are more than one pieces of this type on a face.
E.g. `centre U` on a Megaminx is fully sufficient but for a startip on a FT Starminx you have to write U-R-F to name the startip on face U adjacent to corner U-R-F

Here follow some examples:


EDIT: Thank you for the feedback, especially for some corrections by Burgo's PM! I have added the chapter about piece names following Burgo's suggestion.
Yesterday, I was probably in a hurry starting my Multidodecahedron assembly

EDIT2: Added a comment about different colour schemes in the Motivation paragraph.

EDIT3: I want to repeat the link to Brandon's script:
http://www.brandonenright.net/cgi-bin/gb_util.pl
The script translates Gelatinbrain to either Gelatinbrain (comments are extracted) or TPD Notation.

Konrad,

Thanks very much for putting this together. It's very clear, easy to understand and pretty comprehensive. Much appreciated.

The only minor thing is under face names, you wrote "L (right)" where i think you mean left.

Hi Konrad,

thank you for the great work. It is good understandable, I think.

Cheers,
Andrea

I have made a few updates in my post above and have integrated the feedback I got so far.

This double post wants to draw your attention to text and pictures above in pdf file.
I hope it is good for something.
Feel free to use it wherever you want!

EDIT: I updated the pdf file.
It includes now a reference to Brandon's Sequence Utility at the end.