Two Polyhedra, One Vertex Set

thingiverse

Two distinct polyhedra are formed using the same set of 15 vertices, yet they exhibit contrasting appearances. These two polyhedra combine to create a distorted hexagonal prism that clearly shares a common vertex set. The 15-vertex subset originates from a dissection of the dodecahedron. By adding four vertices above and four below this 15-vertex set, two different polyhedra are created featuring regular polygons as faces. Each resulting polyhedron boasts 19 vertices, six pentagonal faces, three square faces, and ten triangular faces. When these polyhedra are combined, they form a dodecahedron, highlighting their connection to the three-fold symmetry pair found in thing:1380887. The provided OpenSCAD code facilitates this creation process. Print Settings: Printer Brand: MakerBot Printer: MakerBot Replicator (5th Generation) Rafts: Doesn't Matter Supports: No Resolution: 0.3 mm OpenSCAD's "hull" command generates the distorted hexagonal prism formed by combining the two polyhedra from the 15-vertex set, which is essentially the convex hull of this vertex set. Refer to https://en.wikipedia.org/wiki/Convex_hull for further information. Using OpenSCAD's "hull" command on either polyhedron produces the same distorted hexagonal prism, demonstrating its versatility in creating unique geometric shapes.