The 0s are rhythm — clock edges, not phases. One full cycle: a +1 IN rising edge opens it, the work spins through 4 distinct phases (90·180·270·360), and a +1 OUT falling edge closes it — returning to 0. Two ticks bracketing four phases. Edge · Work · Edge. One duty cycle.
A line has two different endpoints. A cycle returns to its start — so its two ends are the same point in space (360° = 0°) but different ticks in time (the in-edge that opens, the out-edge that closes). That's what makes it a cycle and not a line. The two 0s aren't a double-count; they're the two edges of one period — and a period needs both.
Per side: 27 = 1 + 26 — one boundary card (the edge / the tick) plus 26 operations (the work between ticks). The boundary isn't bolted on; it's the 27th member that completes the cube (27 = 3³). Two sides — IN and OUT — mirror across the gap, and the rotation carries you from one edge to the other and home again.