Building a 3x3x3 LED cube?

I need to built a 3x3x3 LED cube. I need to be able to turn every LED on (not at the same time) in different patterns. I need to use Charlieplexing (note that any other method is not a viable option), with a Arduino UNO (6 pins). I am allowed to use soldering. I have a limited supply of components:

• 6 Resistors
• 1 Arduino Uno
• 27 LEDS
• Soldering iron and solder
• Few wires (these wires cannot be used to connect the LEDs to each other. I need to solder)

How would I go about doing this? Please refrain from suggesting ideas that require components not listed above and do not use Charlieplexing. I searched online but found very tutorials with the above constraints. One useful tutorial was:

http://tomscircuits.blogspot.ca/2010/10/charlie-cube.html

However the above tutorial uses transistors, something that I do not have. It also doesn't show where the pins need to be placed. I was also hoping for something with a bit more detailed instructions. This is not a homework assignment.

Please do not suggest examples (there are a plethora of videos and images of cubes online) but rather some kind of guide or instructions on how to proceed.

I unfortunately have no ideas. I was able to Charlieplex 27 LEDS successfully - however this was all on one layer as opposed to being a cube. Charlieplexing on one layer was simple - just a matter of connecting wires, however Charlieplexing with a cube seems to be much more complex.

• 27 LEDs are 27 LEDs, however you arrange them. – starblue Dec 26 '12 at 23:13
• @starblue I agree, but arranging them in a cube is much more complex as it requires soldering and a completely different "pattern". Concepts used for the one layer cannot necessarily by applied to a 3D cube as the connections are completely different in shape (in the first case the connections are 2D however in the latter case, the connections are 3D). I have never worked with 3D structures or soldering before, which could possibly be why I find this so complicated. – dfg Dec 26 '12 at 23:20
• Some of your requirements seem to be for religious reasons only since they appear arbitrary and pointless. For example, you say this is not homework, then you say you are only "allowed" to use certain methods. This leaves the strong impression you are being less than truthful or are deliberately withholding information. This is therefore not a real question and needs to be closed. – Olin Lathrop Dec 26 '12 at 23:20
• @OlinLathrop I assure you this isn't homework. My math teacher told me about a science contest he had in university, where he was given a list of projects to choose from. He built the project mentioned above, and he suggested I try it out as an exercise. I do not see why the question should be closed - what rule does it violate? Its on topic, objective and contrary to what you believe, is truthful. – dfg Dec 26 '12 at 23:25
• To downvoters - I would appreciate a reason as to why you felt this question deserved to be down voted. I have provided sufficient and valid responses to any problems brought up in the above comments. – dfg Dec 26 '12 at 23:27