You are standing on a Goldberg polyhedron: a sphere tiled by 40,962 cells — 40,950 hexagons and exactly 12 pentagons. The view is a gnomonic projection of the tiles around you, which is why the grid looks flat underfoot and stretches toward the edges. You are really walking on a sphere.
Euler's formula forces any hexagonal tiling of a sphere to contain exactly twelve pentagons — they sit at the corners of the underlying icosahedron and cannot be removed. Find all 12. Each one you step on is marked in amber and counted under Relics.
| WASD / arrows | step to the adjacent tile in that screen direction |
| QEZC | step along the four diagonal hex directions |
| click a tile | walk the shortest path to it |
| scroll / +- | zoom the projection |
| F1 ? H | open or close this manual |
| Esc | close this manual |
| six-way pad | the hexagonal pad at the bottom right steps in each of the six hex directions |
| tap a tile | walk the shortest path to it |
| pinch | two fingers on the map zoom the projection |
| + / − | zoom in fixed steps |
| ? | reopen this manual |
| Explored | tiles revealed of all 40,962. Walking reveals a 3-tile radius. |
| Position | latitude / longitude of your cell on the sphere |
| Cell | hex or pent plus the cell's index — a pentagon announces itself here before you see it |
| dark empty tiles | unexplored ground; outlines only |
| amber outline | a pentagon you have found |
| minimap | orthographic globe of the hemisphere you are on, showing explored terrain |
The twelve are spread evenly — icosahedral vertices, roughly 63.4° apart. From one pentagon, the nearest five are about 1,100 tiles away, so they are not stumbled upon by accident. Watch the grid instead: near a pentagon the surrounding hexagon rows converge and the rings tighten noticeably. Terrain is no guide — they fall wherever they fall, including under the ocean.
Press F1 any time to return here.