Triangular Pocket Prism
This puzzle is equivalent to the commercially produced game called Rubik's Ufo.
Java Applet Instructions

The Green Flag resets the puzzle.

Pressing the Spacebar scrambles the puzzle.

Down Arrow turns the bottom six cubelets by 180 degrees. The
same can be achieved by clicking on the top of the corner piece.

Right Arrow turns the right six cubelets by 180 degrees.
The same can be achieved by clicking on the top of the rightmost piece.

Left Arrow turns the left six cubelets by 180 degrees. The
same can be achieved by clicking on the top of the leftmost piece.

Pressing a turns the top layer by 120 degrees clockwise.
The same can be achieved by clicking on the leftmost face of this layer.

Pressing y or z turns the top layer by 120 degrees
counterclockwise. The same can be achieved by clicking on the
rightmost face of this layer.

Pressing s turns the bottom layer by 120 degrees clockwise.
The same can be achieved by clicking on the leftmost face of this layer.

Pressing x turns the bootom layer by 120 degrees counterclockwise.
The same can be achieved by clicking on the rightmost face of this layer.

Klicking on the top of one of the central edge triangles turns
the entire edge/side by 180 degrees.

Pressing q flips the entire prism over by 180 degrees
in the direction back > right.

To solve the prism, you have to get the top side yellow,
the left side blue and the right side red. (The green back and the white
bottom are invisible.) When you solve it, your time taken is displayed
for 5 seconds.
Solution Strategy

First get one corner column right. This can be done intuitively
by moving the two pieces into their respective positions. For instance,
start by solving the left column: greenyellowblue on top,
bluewhitegreen at the bottom.

Secondly, get one of the remaining four corner pieces into its
correct position. For instance, let us assume that the bottom top
piece (yellowredblue) is correct. Then the third top corner
(the right one) is either in the correct (right) column or the bottom
front piece. In the latter case, use D'  R  D to get it
where it belongs.

Now the only possibly incorrect corner pieces can be the ones
at front bottom and right bottom. To interchange them, use
R  U  F  U'  R. Then the three corner columns should be
correct.

If two of the middle columns need to be turned upside down, use
RLFRLF or LRFLRF etc. The starting two directions
should be the ones nearest to the two inverted columns.

Usually the edge pieces will be permuted in a more complicated fashion.
You can cycle three at a time using the following move.
To cycle (left top > back top > back bottom > left top) use
(R U' R U R)  (L U' L U L)  U  (F L R F L R). Similar moves can be
devised for other 3cycles. Or you bring the desired three edge pieces
to the indicated positions and move them back after finishing the
algorithm.

Easier moves to permute edges may be possible. Please tell me
about your discoveries!