The International Fixed Calendar is an alternative to the Gregorian Calendar that we all know and love (hate? hate.) It was proposed by Moses Cotsworth in 1902. He created the International Fixed Calendar to solve common problems caused by the traditional Gregorian Calendar:
The International Fixed Calendar uses the same year numbering and number of weekdays as the Gregorian Calendar. However, the calendar is divided into 13 months with 28 days, giving each month exactly 4 weeks. The thirteenth month, Sol, is between June and July. Every year and month begins on a Sunday, so the same date in each month or year will always be on the same week day as well.
International Fixed Calendar Leap Years work similarly to Gregorian Leap Years: every 4th year, except in years that are divisible by 100 but not divisible by 400. The leap day is added to June instead of February. The extra day has no week day name (e.g., "Sunday" or "Monday") but is instead called "Leap Day". It happens between the last Saturday of June and first Sunday of Sol.
If you're doing the math, you probably noticed that 13 months x 28 days = 364 days per year. Where is the extra day? The extra day is added to the end of December. Like Leap Day, December 29th has no named week day but is called "Year Day" instead.