3D Cairo Tiling

Hi All,

I've been trying to create 3D Cairo Tiling - so cairo tiling where three points from every pentagon meet in the Z axis to form 3 diamonds.

I have done this by getting the centre-point of each cairo tile, moving it in the Z axis and then attaching it to the 3 nearest points on the cairo tile. It has been quite successful however not every diamond is completed and some of the diamonds are being finished incorrectly. Does anyone know how to solve this problem?

Also once I have created these 3D cairo tiles from lines how would I create surfaces from the lines?

Thanks guys

Sarah