Twenty-four boxes make one day. Arranging them so they form a ring forms a 24-hour analog clock dial.
In nature, time is linear, but the circular motion of our planet around its axis and about the Sun shapes our perception of our time to be cyclic. To measure our productivity and keep track of the passage of time, we have devised tools like clocks and calendars. Though we have rendered this cyclic perception of time well into rotating hands of a clock, the transition of this metaphor fails as we move to a more linear depiction in a calendar. This thought germinated the idea of a continuous representation of a clock into a week or a month of a calendar.
Instead of taking a traditional 12 hour clock face, I chose a 24-hour clock circle as it is a better middle ground between an hourly distribution of time by a clock and daily distribution by a calendar. Each hour of the day is depicted with a notch/box on the ring, thirty such rings would form a month. By putting these equidistant from each other such that the 2am hour face towards a common center forms a larger ring/toroid for a month.
With the 2am hour of each ring facing towards common center, the toroid formed depicts the day/night contrast. The day hours are easily visible on the outer side of the toroid, and can be marked with availability. The night or sleep hours on the other end are hidden in the inner part as they need no depiction for availability.
As one day changes to next seamlessly with the passing hour, this same transition can be depicted in the current model through a toroidal helix.
If the trajectory of lat-long of a place is plotted around the Sun, then the shape formed would be an epitrochoid, with 365 minute bumps making a year. If these are scaled up, they will form overlapping loops, with each loop representing a day. And a 24th section of each loop will represent an hour of the day.