AntiCube was suggested by Jason Smith. It has the geometry of a square antiprism. Some fudging was needed to make everything fit. This twisty puzzle has ten turning faces: two square and eight triangular. It has only edges, that turn over and under each other in unexpected ways.

Watch the YouTube video
Read at the Shapeways Forum
Read more at the Twisty Puzzles Forum

Please contact Oskar directly if you are interested in obtaining a fully colored, stickered and assembled sample of this puzzle.