High Quality Content by WIKIPEDIA articles! The Trapezo-rhombic dodecahedron is a convex polyhedron with 6 rhombic and 6 trapezoidal faces.This shape could be constructed by taking a tall uniform hexagonal prism, and making 3 angled cuts on the top and bottom. The trapezoids represent what remains of the original prism sides, and the 6 rhombi a result of the top and bottom cuts.A space-filling tessellation (or honeycomb) can be made by translated copies of this cell. Each "layer" is a hexagonal tiling, and alternate layers are connected by shifting their centers so the rhombic faces match up.It is the polyhedral dual of the triangular orthobicupola.

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