Three axes, each its own bit, none folded into another: cardinal (which way), colour (blue / red), phase (solid / hollow). Bind any two and it collapses — 16 → 8 → 4 → 2. Held apart, it is the full 4-cube.
what this is, honestly: not a new object. Sixteen symbols as 4 sides × 2 colours is a Wang tile set (Wang, 1961; Ammann's classic set is exactly 16), and the structure underneath is the 16 vertices of the tesseract Q₄ — the 4-bit strings, each axis one bit. The cardinal/colour/phase reading is your labelling; the maths is standard. Each glyph's code below is its hypercube address: cardinal(2) · colour(1) · phase(1).
why phase is solid/hollow, not a flip: "inverted" as a literal vertical flip is the U↔D swap — already two of the cardinals. Used as phase it re-binds and the count falls back toward 2. Realising phase as an attribute the rotation can't reach (solid vs hollow) is the one move that keeps the fourth bit free. That, not the count, is the whole content of "unbind."