join their ends to form a Möbius strip. Thus the 16-cell can be decomposed into two cell-disjoint circular chains of eight tetrahedrons each, four edges long, one spiraling to the right (clockwise) and the other spiraling to the left (counterclockwise). The left-handed and right-handed cell rings fit together, nesting into each other and entirely filling the 16-cell, even though they are of opposite chirality. This decomposition can be seen in a 4-4 duoantiprism construction of the 16-cell: or , Schläfli symbol {2}⨂{2} or s{2}s{2}, symmetry [4,2+,4], order 64. Three eight-edge paths (of different colors) spiral along each eight-cell ring, making 90° angles at each vertex. (In the Boerdijk–Coxeter helix before it is bent into a ring, the angles in different paths vary, but are not 90°.) Three paths (with three different colors and apparent angles) pass through each vertex. When the helix is bent into a ring, the segments of each eight-edge path (of various lengths) join their ends, forming a Möbius strip eight edges long along its single-sided circumference, and one edge wide. The six four-edge halves of the three eight-edge paths each make four 90° angles, but they are not the six orthogonal great squares: they are open-ended squares, four-edge 360° helices whose open ends are antipodal vertices. The four edges come from four different great squares, and are mutually orthogonal. Combined end-to-end in pairs of the same chirality, the six four-edge paths make three eight-edge Möbius loops, helical octagrams. Each octagram is both a Petrie polygon of the 16-cell, and the helical track along which all eight vertices rotate together, in one of the 16-cell's distinct isoclinic rotations. Each eight-edge helix is a skew octagram{8/3} that winds twice around the 16-cell and visits every vertex before closing into a loop. Its eight edges are the circular path-near-edges of an isocline, a geodesic arc on which vertices move during an isoclinic rotation. The isoclines connect opposite vertices of face-bonded tetrahedral cells, which are also opposite vertices (antipodal vertices) of the 16-cell, so the isoclines have chords. The isocline winds around the 16-cell twice (720°) the way the edges of the octagram{8/3} wind around twice, passing alongside each of the edges once, and alongside each of the orthogonal axes of the 16-cell twice. The eight-cell ring is chiral: there is a right-handed form which spirals clockwise, and a left-handed form which spirals counterclockwise. The 16-cell contains one of each,