An independently discovered THEORETICAL fourth dimensional analogue of the Gyroelongated Square Pyramid. That is, I don't know enough about mathematics to know it it's possible, just enough to imagine it. When projected at the right angle (that at the beginning and end of the video) the shapes' edges match up perfectly with the ones on Metatron's Cube.
http://www.lokiclock.com/still/3dren/j4d/index.shtml
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