Philosophers commonly refer to chiliagons to illustrate ideas about the nature and workings of thought, meaning, and mental representation.

A regular chiliagon is represented by Schläfli symbol {1,000} and can be constructed as a truncated 500-gon, t{500}, or a twice-truncated 250-gon, tt{250}, or a thrice-truncated 125-gon, ttt{125}.

Therefore, construction of a chiliagon requires other techniques such as the quadratrix of Hippias, Archimedean spiral, or other auxiliary curves.

René Descartes uses the chiliagon as an example in his Sixth Meditation to demonstrate the difference between pure intellection and imagination.

[1] Philosopher Pierre Gassendi, a contemporary of Descartes, was critical of this interpretation, believing that while Descartes could imagine a chiliagon, he could not understand it: one could "perceive that the word 'chiliagon' signifies a figure with a thousand angles [but] that is just the meaning of the term, and it does not follow that you understand the thousand angles of the figure any better than you imagine them.

[4] Immanuel Kant refers instead to the enneacontahexagon (96-gon), but responds to the same question raised by Descartes.

[7] The regular chiliagon has Dih1000 dihedral symmetry, order 2000, represented by 1,000 lines of reflection.

For example, the regular {1000/499} star polygon is constructed by 1000 nearly radial edges.