It was discovered through play that by wrapping the outlying vertices of a group of tessellated Rhombic Dodecahedra with a convex hull, an approximation of a Truncated Octahedron was produced. Upon further investigation, it was discovered that an approximation of a Rhombic Dodecahedron emerged by wrapping the outlying vertices of a group of tessellated Truncated Octahedra with a convex hull.

# Tag: rhombic dodecahedron

A space-filling polyhedron is one that can be used to generate a tessellation in space. That means that by duplicating and translating (not rotating) the shape, we can create a three-dimensional tiling that leaves no gaps between its constituent shapes. This is of course easy to visualize with a cube; things begin to get both messy and interesting when you explore tessellations with other non-platonic space-filling shapes. And so began my brief but exciting journey into the lands of the Rhombic Dodecahedron.