Root-Two Rhombus Polypanel

myminifactory

The "Root-Two Rhombus" boasts identical side lengths but distinct internal angles compared to Devin Montes' polypanel rhombus, making all the difference in how well it interacts with its three-dimensional duplicates. This rhombus can be joined together in numerous ways without creating gaps that nothing fits into, a problem its counterpart is prone to. I call this polypanel the "Root-Two Rhombus" due to its diagonals featuring lengths in the ratio 1:√2. Its internal angles work out to approximately 70.5 and 109.5 degrees. In contrast, the original rhombus has internal angles of 120 and 60 degrees. One of the shapes that can be crafted from the Root-Two Rhombus is a rhombic dodecahedron, an attractive symmetrical shape with interesting mathematical properties because it tiles space. Twelve Root-Two Rhombuses are required to construct a small rhombic dodecahedron measuring about 10 cm wide. To create a rhombic dodecahedron twice as large, four of these rhombuses can be used to construct each face, requiring a total of 48 rhombuses. To build one that is three times as large, nine rhombuses can be used to construct each face, necessitating a total of 108 rhombuses, and so on. The faces remain relatively rigid even when composed of smaller rhombuses. A practical application of these rhombuses lies in creating a lampshade as Devin did with some of his polypanels. However, using Root-Two Rhombuses allows for the creation of a perfectly symmetrical shape using only one type of polypanel. Additionally, connecting the rhombuses around the cable of the lamp requires no special connecting panel. The light bulb shines through the gaps in the polypanels to create little star patterns on the walls, which is quite appealing. The connectors on the edges of the Root-Two Rhombus are derived directly from Devin's "Polypanels_Snaps Only" design, and their positioning conforms to the polypanel standard so that they will connect properly with any other polypanel. In keeping with the ethos of polypanels, my design doesn't require any supports to print, which reduces waste. I've also included variants of the rhombus featuring a receiving ring compatible with the Polypanel Face-Snap System (#PPFSS), allowing you to snap specialty panels into it or connect the face of the rhombus to the face of other compatible polypanels.