The Teglon

The Teglon is a classical geometric challenge rooted in the culture of the Halls of Orithena. It is closely associated with the decagonal forecourt called The Decagon and with the theoric figure Metekoranes. The term also appears in accounts of a very old Lineage (rumored tradition) devoted to preserving and pursuing the problem.

Components and Layout

• Board: a flat, decagonal plaza (a very large ten‑sided court) traditionally used as the playing surface.
• Tiles: seven distinct molded shapes made of baked clay. Each tile carries a shallow groove that runs from one edge to another so that adjacent tiles’ grooves can join into longer curves. Reproduction sets are in use at the site, and original molds have been recovered during the excavation.

Objective and Play

Starting from one chosen vertex of the Decagon, the player places tiles so as to pave the entire surface. The shallow groove on the tiles must connect to form a single continuous, unbroken curve that begins at the starting vertex and ends at the opposite vertex, and the curve must pass across every tile in the completed paving.

Practical obstacles arise as the pattern grows: interior placements constrain later choices, and segments of unconnected groove often need to be left temporarily and then rejoined by careful steering of subsequent tiles.

Theoric Significance

Ancient Orithenans suspected that the seven‑tile system is aperiodic (non‑repeating), making straightforward periodic solutions impossible. Tradition holds that Metekoranes believed the final pattern exists in the Hylaean Theoric World (ideal forms realm) and that only a mind able to apprehend that whole could truly “solve” the Teglon.

Associations and Practice

• Metekoranes is remembered in connection with the Decagon at Orithena during the ash fall that buried the site.
• Around the plaza, modern keepers assemble small demonstration patterns from reproduction tiles and invite careful experimentation on the Decagon’s edge.

Notes

• Terminology: People sometimes use “the Teglon” to mean the Decagon itself; here, “Teglon” refers to the problem, while the place is The Decagon.
• Ambiguity preserved: No general solution is credited; the problem is described as inspiring intense study and, in some accounts, unhealthy fixation.