Production time depends on the size of the design and the chosen finish. If a model is larger than 56 mm in all dimensions the production time is 15 business days with Priority manufacturing. For smaller models, the production time is 11 business days with Priority manufacturing. The shipping time depends on your location.

Platinum models are 3D printed using a complex five-step process. First, the model is printed in wax using a specialized high-resolution 3D printer. It is then put in a container where liquid plaster is poured in around it. When the plaster sets, the wax is melted out in a furnace, and the remaining plaster becomes the mold. 
Molten Platinum is poured into this mold and set to harden. The plaster is broken away, revealing your new product. The product is then carefully cleaned and hand-polished to give it the trademark Platinum luster. Please be aware that polishing can wear down or fill in very fine details and edges. Polishing also removes a bit of material from your product in order to smooth it out, so the exact volume may be up to 10% smaller than that of your digital model.

https://www.shapeways.com/materials/platinum