Eventually he chose a design for the building as a geometric pentagon – a building with five sides – and that's why the building is called the Pentagon.
The significance was that that constant didn't depend on the shape itself, it could have been a square, or a cat, or the pentagonal faces of our dodecahedron, whatever.
The cathedral garth was a cloistered, pentagonal garden with a bronze postmodern fountain. Katherine was amazed how loudly the fountain's flowing water seemed to be reverberating in the courtyard.
Gawain's integrity and honor, symbolized by his heraldic device of a pentangle, are at stake in the Adventure of the Green Chapel, and what chiefly threatens to impair them is fear of the Green Knight's axe.