#mefferts

This is a Meffert gear ball. It has 3 orthogonal axes of rotation. These 3 axes pass through the centre of the ball.    

Here we have my rough digital picture of the cube. As we explore different orientations, assume the side colour corresponds to the center piece (and not the colour with most majority on the face). 

First we must establish a frame of reference for exploring the cube. Let’s choose an arbitrary starting position for the ball: the red face is towards you, and the yellow face is on top. The green face is now the right face. Call the red face the front face, symbolised F. Call the top face the upper face, symbolised U. Call the green right face ‘R’.  

Here we will note that in order to maintain consistency this tutorial assumes you will hold the cube with your left thumb on the red center and your left middle finger on the purple center, turning always with your right hand. 

Now, we must establish universal language to refer to the different types of moves we can make with the ball.

The first rotation is a clockwise quarter turn of the right hand row, and should result in the following appearance of the front face:

  This move will be referred to as R and the reverse (anticlockwise) of this move shall be called R- (minus). R- produces the same result with the orange and yellow colours reversed. 

The second rotation is a rotation of the upper row and will be referred to as rotation U.

Note that in all the positive moves your thumb advances forwards/away from you while in a negative move the thumb is travelling backwards. Thus, for left handed people, the puzzle can be held in the right hand and turned with the left hand, and by negating every move shown the same results will occur (due to the dual rotation property of the ball).  

For the last rotation, rotation F, the position in which you hold the ball must be altered a little so your right thumb holds the blue center while your middle finger holds the green center. 

Now that these simple moves are established, we can move on to creating modules of moves which in combination can be used to effectively solve the ball. The first module of moves is the sequence R U U R- or R U2 R-.

Here is a display of the appearance of the cube after these moves are implemented. Note that the pink coloured move is a suggestion which will align the edges of your gear ball.  This module is commonly used to swap two centers. Note how our front face, Red, is now solved excluding the center piece. Thus, in the situation where we need to swap around two center pieces in order to solve the puzzle, this move would be appropriate. Have fun exploring the power of this move sequence! The second module of moves, RUFRUF, deals with the inner C-shaped pieces. 

After performing RUFRUF on the solved cube, a pattern emerges. We can use knowledge of this pattern to then apply RUFRUF in a situation where the inner pieces are out of place.  Note that the top and bottom faces match while the middle 4 faces only match each other. This is a common outcome of ordering the cube. Even solving for only one face will usually produce the pattern of 2 solved faces and 4 identical/patterned middle faces.  The last useful move sequence is RURURU.

As shown, this module does not affect the chosen front face. It reverses all tiles on the upper face excluding a diagonal running from top left to bottom right. If the 4 middle faces are observed by turning the cube while holding the top and bottom a zigzag pattern has been created. Recognizing this pattern while solving the cube will allow you to reverse the desired tiles.  Now we are ready to create a full solving strategy.

1. Orient the ball and observe frames of reference such as the desired top and front faces.  2. Create order by solving all corners and centers (simple) 3. Observe resulting patterns and implement the above modules until a solution is reached. 

What patterns can you make with the Meffert Gear Ball?