The International Week Calendar (IWC) is a subset of the International Calendar (IC), hence a standardized variant of the proleptic Gregorian calendar (PGC), more specifically ISO week date. The International Standard Week Calendar (ISWC) is a limited specialization of the IWC. It runs in parallel with the International Month Calendar (IMC).
The week year has exactly 52 weeks (364 days) in a short year or 53 weeks (371 days) in a long year.
Each of the 4 quarters, called quarts, has 13 weeks excatly, except for the final one in long years. This long quart has 14 weeks then.
Although there is no consensus on how quarts of 91 days or 13 weeks should be separated into 3 months of almost equal length, there are just two basic approaches: one divides each quarter into portions of 30 days twice and 31 days once, the other uses 4 weeks twice and 5 weeks once. Choosing the former, the Common-Civil-Calendar-and-Time calendar, the ISO-Uncia Leap Week Calendar and the Edwards perpetual calendar all use 30:30:31 days, the Symmetry010 Calendar uses 30:31:30 days and the Aristean Calendar uses 31:30:30 days. When the “Thursday rule” is applied to any of these patterns it always results in a week layout of 4:5:4 as in the Symmetry454 Calendar, i.e. neither 5:4:4 as in the Bonavian Civil Calendar nor 4:4:5. Months of quarts, furthermore, cannot match exactly hypothetic full-week months of the IMC, because the first triad sometimes would have just 12 weeks and the third triad may also have 14 weeks (like the fourth).
Quarts are therefore divided into three months that primarily consists of 4, 5 and 4 weeks and, matching that middle-high scheme, alternatively they consist of 30, 31 and 30 days. Without weeks or days provided, there is no distinction between these – the month duality. There is no way to reference a day in 28|35-day months without its week.
The week year is also divided into 13 months, called moons. A normal moon has 4 complete weeks (28 days). The last moon in long years is a long moon and has 5 weeks (35 days). Since there is a leap week instead of intercalary days, these moons align with the week year of the IWC, not the month year of the IMC.
This format is compatible with the New Earth Calendar, which uses a custom leap rule though, and differs from the International Fixed Calendar (Cotsworth–Eastman plan), which uses intercalary days and starts weeks on Sunday.
With alternative leap rules, there could be a 13-moon year with an additional leap moon every 22 or 23 years, but this does not work with a 400-year leap cycle, because it does not contain an integer multiple of 28 days. The 293-year cycle, however, would contain exactly 13 leap moons. Another leap rule may use an independent year count for moon years, of which there are 294 in a cycle of 293 week or month years. There would be no long moons in either case.