I thought I'd have a go at describing the power structure of classical Athens. Thinking caps on...this is complex.
Sovereign power was held by the ecclesia, and only by the ecclesia. It was a parliament consisting of every single voting member of the state. This is what makes Athens the world's first democracy. Athens was a direct democracy; you didn't elect someone to represent you; instead you turned up to vote for yourself. Ecclesia remains a word in English to this day and means a collection of churchmen. The church term comes directly from the original Athenian parliament.
There were maybe 25,000 eligible voters. Obviously they didn't all turn up for every session. The quorum for a valid vote was 6,000. On days when there wasn't much happening, they struggled to get enough voters to turn up, so the Scythian Guard would sweep through the agora with a long rope covered in wet paint, to herd the voters to parliament. Since the Scythian Guard was all slaves, this meant slaves were going around forcing their owners to run the city.
That was the simple bit.
25,000, or even the minimum 6,000 makes for a very large meeting. To keep things moving, they had a parliamentary management committee called the boule. Boule means council. They met at the bouleterion. Just about every city in Greece had a building by this name. Even the site for the Olympic Games had a bouleterion.
Everyone in Athens had to belong to one of the ten tribes, which by classical times were purely administrative units. Every year, 50 men were elected from each tribe to be members of the boule. That makes a management committee of 500 people. Clearly the Athenians liked to do things big. Since the boule set the agenda for the ecclesia, the members of the boule should have been very powerful. Their large membership and only holding the office for a year kept them in check.
Since boule membership only lasted a year, you could cycle through the entire voting population in 50 years. Obviously not everyone got a go on that scheme, but the great majority would have.
Because 500 was still too large, they had a management committee for their management committee. They selected 5 men from each of the ten tribes represented in the boule to form a subgroup called the prytaneis. So that made 50 men in the prytaneis. They rotated membership of the prytaneis each tenth of a year. So if you were elected to the boule, you'd spend 36 days as a prytaneis.
The good news for the prytaneis was, they ate for free -- at public expense -- because they were required to spend their 36 days living in a building in the agora called the Tholos. The Tholos gets a mention in The Pericles Commission because they were building it at the very moment the book begins. Most unusually for Athenian architecture, it was designed as a perfect circle. Members of the prytaneis could call a meeting of the ecclesia -- the entire citizenry of Athens -- at any time. In effect, the prytaneis could press the emergency alert button. Which in a few crisis situations they did.
So: Athens was ruled by the ecclesia of about 25,000 voting citizens. The ecclesia was managed by the boule of 500 citizens. The boule was managed by 50 of their number called the prytaneis.
Athens had a very clear distinction between sovereign and executive power. Much clearer than in modern times, when we tend to mix them up. Executive power was wielded by the archons for civil matters and the strategoi for military. Neither had any say (in theory) on what the people decided. I'll save those for another day or this post will get way too long.