Myriagon


In geometry, a myriagon or 10000-gon is a polygon with 10,000 sides. Several philosophers have used the regular myriagon to illustrate issues regarding thought.

Regular myriagon

A regular myriagon is represented by Schläfli symbol and can be constructed as a truncated 5000-gon, t, or a twice-truncated 2500-gon, tt, or a thrice-truncated 1250-gon, ttt

Symmetry

The regular myriagon has Dih10000 dihedral symmetry, order 20000, represented by 10000 lines of reflection. Dih100 has 24 dihedral subgroups:,,,, and. It also has 25 more cyclic symmetries as subgroups:,,,, and, with Zn representing π/n radian rotational symmetry.
John Conway labels these lower symmetries with a letter and order of the symmetry follows the letter. r20000 represents full symmetry, and a1 labels no symmetry. He gives d with mirror lines through vertices, p with mirror lines through edges, i with mirror lines through both vertices and edges, and g for rotational symmetry.
These lower symmetries allows degrees of freedom in defining irregular myriagons. Only the g10000 subgroup has no degrees of freedom but can seen as directed edges.

Myriagram

A myriagram is a 10,000-sided star polygon. There are 1999 regular forms given by Schläfli symbols of the form, where n is an integer between 2 and 5,000 that is coprime to 10,000. There are also 3000 regular star figures in the remaining cases.

In popular culture

In the novella Flatland, the Chief Circle is assumed to have ten thousand sides, making him a myriagon.