Midpoints
Every pair of chart points has a degree halfway between them. This page lists all of them in zodiacal order, then every natal point standing on a midpoint axis — at the midpoint or any multiple of 45° from it. Same birth data as the birth chart, shareable straight from the URL.
What a midpoint is
Take any two chart points and there are two degrees of the circle equally distant from both, one on each side. The one reached halfway along the shorter arc between them is the midpoint listed here; the degree directly opposite it is the same axis seen from the other side. The arithmetic is a half-sum with a wrap: the Sun at 10° Aries and the Moon at 10° Gemini put the midpoint at 10° Taurus, 30° from each.
A midpoint is read as an axis rather than a single degree. Together with the degrees standing 45°, 90°, and 135° from it, the midpoint and its opposite divide the circle into eighths, so the contact table flags any natal point within orb of any multiple of 45° of separation from the midpoint — the set cosmobiology works with. The axis-angle column names which multiple; the orb column says how far from exact.
Twelve points — the classical ten plus the Ascendant and Midheaven of a timed chart — make 66 pairs, so a timed chart has 66 midpoints; without a birth time there are no angles, leaving ten points and 45 pairs.