The "Root-Two Rhombus" has the same side lengths but different internal angles to the polypanel rhombus created by Devin Montes, and this is an important difference because it allows this rhombus to play more nicely with copies of itself in three dimensions in the sense that there are many more ways they can be joined together without ending up with a gap that nothing fits into, which is a problem the other rhombus is prone to.
I call this polypanel the "Root-Two Rhombus" because it has diagonals with lengths in the ratio 1:√2. It's internal angles then work out to be approximately 70.5 and 109.5 degrees. By comparison, the original rhombus has internal angles of 120 and 60 degrees.
One of the shapes you can make out of the Root-Two Rhombus is a rhombic dodecahedron, which is a nice symmetrical shape that is interesting mathematically because it tiles space. Twelve Root-Two Rhombuses are required to build a small rhombic dodecahedron that is about 10 cm wide. To create a rhombic dodecahedron that is twice as large, you can instead use four of these rhombuses to construct each face, requiring a total of 48 rhombuses. To create one that is three times as large, you can use nine rhombuses to construct each face, requiring a total of 108 rhombuses, and so on. The faces remain relatively rigid even when composed of smaller rhombuses.
One practical application of these rhombuses is to create a lampshade as Devin did with some of his polypanels, but with Root-Two Rhombuses, you can make the lampshade's shape perfectly symmetrical and only using one type of polypanel. You can also easily connect the rhombuses around the cable of the lamp without any need for a special connecting panel. The light bulb shines through the gaps in the polypanels to create little star patterns on the walls, which is quite nice.
The connectors on the edges of the Root-Two Rhombus are derived directly from the "Polypanels_Snaps Only" design provided by Devin, and the positioning of these connectors conforms to the polypanel standard so that they will connect properly with any other polypanel. And 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 that have a receiving ring that is compatible with the Polypanel Face-Snap System (#PPFSS) so that you can snap specialty panels into it or connect the face of the rhombus to the face of other compatible polypanels.