Summary

This looks like WiggleLamp6 but it is based on totally different geometry. The base also accommodates a wall power driven LED kit. Here are sources for different kinds of LED lights, all of which work with this design:

https://www.superbrightleds.com/moreinfo/surface-puck-lights/3-watt-led-puck-light-fixture/2085/

http://www.amazon.com/gp/product/B00R7F7PNQ?psc=1&redirect=true&ref_=oh_aui_detailpage_o01_s00

http://www.lowes.com/pd_406110-43768-NS511-R6-306_1z0y4gqZ1z10d2u__?productId=4177463&pl=1