The Hexasphere

GeoWords is played on a hexasphere — a 3D sphere made up of hexagonal and pentagonal cells. Think of a soccer ball (football), but with many more faces and rendered as an interactive 3D object you can orbit, zoom, and explore.

How It's Built

The hexasphere is a subdivided icosahedron dual:

1. Start with an icosahedron — a regular solid with 20 triangular faces.
2. Subdivide each face into smaller triangles (the subdivision level controls how many cells the sphere has).
3. Take the dual — replace each vertex with a face, and each face with a vertex. The result is a sphere covered in hexagons and pentagons.

The 12 vertices of the original icosahedron become the 12 pentagonal cells. Everything else is hexagonal.

Cell Count

The number of cells depends on the subdivision level:

GeoWords uses subdivision 6 by default, giving 362 cells.

Cell Anatomy

Each cell has four visual components:

• Face — the flat inner polygon where the letter (or symbol) sits. Independently texturable.
• Bezel — a 45-degree chamfered ring around the cell perimeter. The bezel is the primary visual channel for communicating value and state — its color, intensity, and texture encode information like letter rarity, scoring properties, and selection state.
• Shaft — the side walls visible when a cell is in relief (raised or recessed relative to the sphere surface).
• Symbol — a 3D extruded glyph placed on the face. Each letter is a tessellated mesh generated from font outlines.

Relief

Cells can be displaced radially — pushed outward (positive relief) or inward (negative relief) from the sphere surface. Relief is used to communicate game state:

• Flush (zero relief) — the default. Active, unlocked tiles sit flush with the sphere surface.
• Raised (positive relief) — in Lock Down mode, played words are locked and raised, creating a growing topography that records the player's progress.
• Recessed (negative relief) — used by certain tokens to indicate multi-use tiles.

Relief displacement is radial — cells move along the line from the sphere's center through the cell center, not along the face normal. This ensures adjacent cells at the same relief level share edges seamlessly.

Adjacency

Two cells are adjacent if they share an edge. Hexagonal cells have 6 neighbors; pentagonal cells have 5. Adjacency is fundamental to selection — you select tiles by dragging across adjacent cells.

Pentagons

The 12 pentagonal cells are geometrically necessary (you cannot tile a sphere with only hexagons). In GeoWords, pentagons participate fully in gameplay — they carry letters, can be selected, and behave like any other cell. They serve as spawn points in some game modes.