Lately I have presented a concept of classifying puzzles by symmetry class and piece sets. This concept of piece sets can now be illustrated completely for the 3x3x3. The unmodified 3x3x3 has 3 types of pieces:
Corner, Edges and Faces.
Therefore we can derive 8 different mods from the 3x3x3:

{CEF} represents the unmodified 3x3x3
{CF} is implemented by the simple overlapping cube.
{CE} is implemented by the void cube. Thank you, Mr Okamoto.
{EF} is the edges-only-cube
{F} is the Babyface 1x1x1.
{E} is the edges-only-void-cube
{C} is the 2x2x2
{} is the 1x1x1

And here they are:

This picture was one reason (of two) for me to build the Babyface.

Who else has come how far in collecting this series?

I've never really thought about this. This was really interesting to read.

Alex

I feel very honored!

Hi Andreas,

I like your categorization and example set of puzzles. I have proposed a similar categorization - you can read about it here:
http://robspuzzlepage.com/rearrangement.htm#definitions

- scroll down to #5.

Your symbolism may be easier to follow, and you've also accounted for {}, the 1x1x1, which I did not include,
since I would term it "order 0" - nothing turns, and therefore it is not really a twisty puzzle.

Tanner shall be honored as he deserves!!!

@Rob:
What a page!
I will need some time to consume that.
I find it quite interesting (because its like my approach!!) how you define "order" of a puzzle. Considering that I wondered why you haven't posted here:
viewtopic.php?f=1&t=15258

I like your classification method. Thanks for the pics for illustration!

Could a similar system be used to classify shape mods? Systems I can think of become quickly complicated.

i.e. using capital letters to imply that orientation matters, lower case to imply that it does not.

As far as shape/sticker modifications of the 3x3x3 go:

- the standard cube requires orientation of corners and edges, but not faces {CEf}

- a circle cube is functionally the same, but also requires orientation of faces {CEF}

- a mastermorphix requires center orientation, but now some of the corners require orientation, and others do not {c'EF}
I've used c' to represent an incomplete orientation requirement of corners. The problem here is that, at least to a limited degree, edges don't require permutation, and my system does not reflect that.

- likewise, a fisher cube requires orientation from corners, but only some edges and some faces {Ce'f'}

In any case, I appreciate the simplicity of you organization scheme, and I hope it sees a wide adoption.