This variation on the Rubik's cube is called the Magic Octagonal Prism, or
just The Barrel or The Octagon. In Dutch it is called 'Peperbus', which
means pepperpot. It is exactly the same as the normal cube except that
the four vertical edges of the cube are truncated. The corner pieces of
original cube now have only two colours and the four edge pieces in the
middle layer have only one colour.

The differences make this puzzle a little confusing. It is possible to get
to a position where it seems that two pieces need to be swapped or where
one edge piece needs to be flipped, both of which are impossible on the
original cube.

## The number of positions:

There are 8 corner pieces with 3 orientations each, 12 edge pieces with 2
orientations each, giving a maximum of 8!·12!·3

^{8}·2

^{12} positions. This
limit is not reached because:

- The total twist of the corners is fixed (3)
- The middle layer edge pieces show no orientation (2
^{4})
- The colours of the vertical columns are equivalent (4!)

This leaves 8!·12!·3^{7}·2^{8}/4! = 450,541,700,775,936,000
or 4.5·10^{17} positions.

## Solution:

Use any solution method for the Rubik's Cube to solve it as far as possible.
As mentioned above, there are two situations that may occur that cannot happen
on a normal cube.

**One edge needs to be flipped:** Simply flip that edge and one of the
shaved (monochrome) edges. One neat method (which actually flips 3 shaved edges)
is to hold the barrel with the flipped edge at the UR location, where U is an
octagon face, and do E R E R E R E R, where E denotes turning the horizontal middle
slice to the right (anti-clockwise looking from above).
**Two pieces need to be swapped** To swap two pieces just swap any two of
the shaved columns. For example if the U face is an octagonal face, then RL U2 R'L'
will swap the UF and UB edges. Alternatively R2 F2 R2 swaps the UF and DF edges.

Some people prefer to hold the puzzle so that the last layer they solve is
one with two shaved edges (e.g. the octagonal sides are at L and R). This way
any final flips/swaps only involve pieces of the final layer.