Nick Rauh (Triangulated deltoidal icositetrahedron)

Elevation, plastic drinking straws and embroidery floss

[48 F, 72 E, 26 V] This structure starts with a blue tetrahedron and then at each stage elevates it, which is to say, adds pyramids onto each external surface of the previous stage. In this case, the height of each of the pyramids is chosen to make them all flush at the edges of the previous structure. In this way, the process forms in turn a pink cube, then a green rhombic dodecahedron, and finally a purple deltoidal icositetrahedron. Each polyhedron in this iteration allows the next to be rigid. For the purposes of Polyplane, we’re interpreting the final object as the outermost edge framework given by the purple and green edges, which form a triangulation of the deltoidal icositetrahedron.