What has changed in the Atlas, newest first. New tilings are shown as they arrived; drag to pan, scroll to zoom, or open any of them where it lives.
Bubble tiles
v1.35.024 August 2026feature release
New in the atlas
The tiles are Katsushika Hokusai's, drawn in 1824 and named by Lauren Siegel of MathHappens in 2023; this catalogue follows the 2026 study by John Chase, Will Field and Alex McCluer.
The lines where two faces pass through each other are drawn, on a toggle, and they are not edges: they bound no face, so V, E and F are unchanged.
Changed
A face is coloured by its polygon, on the by-side-count ramp the Euclidean tilings already use, with a violet to magenta arc kept for the star faces.
Fixed
Twenty of the 54 star polyhedra were drawn with holes, filled from the wrong crossing ring, which cost a {12/5} face 18.5% of its area and an {8/3} 8.6%.
Two rows in the catalogue were wrong about what they held, one of them vanishing when you clicked it.
A collection that had not loaded yet could be listed under the wrong geometry, and disappeared when opened.
The one star polyhedron whose signed density cancels to 1 while its faces plainly cross now lists under Density unresolved.
Parametric edge lengths
v1.33.019 August 2026feature release
New in the atlas
Twenty of the 58 take a single parameter and four take six, with the vertex-orbit count running from 1 to 8 across the shelf.
The domino tiles the plane 496 ways, where matching every edge whole allows exactly one: running bond, herringbone and basketweave all need a long side met by two tiles.
27,362 half-polygon tilings have been withdrawn. They were real, but they came from a search that could not divide an edge, so the slices holding them counted a subset while reading as a complete enumeration.
the halved hexagon now stops at k = 6 and the halved pentagon at k = 9: each board lists only the k it can enumerate with divided edges allowed
nothing else changed shelf: the halved triangle, the second hexagon cut and the domino were already inside their own ceiling
Fixed
A fifth of the 45-45-90 shelf was being discarded before it shipped. That shelf recognised two tilings as the same by comparing a small patch of each, and at 16 tiles per cell a patch that size cannot tell them apart; the comparison is now exact.
Squares on that shelf were filed as triangles, so picking the square in the polygon filter never found them.
Five old links work again. A de-duplication pass had absorbed those families into more general ones without leaving a redirect, so each one opened on nothing.
{3,7} and {3,8} cut by an altitude; {4,5}, {5,4}, {6,4} and {4,6} cut by a diagonal.
Which boards exist at all is a counting question: a vertex-transitive tiling needs 2q/p diagonal ends at the average vertex, so it has to be a whole number.
Half hexagon on the long diagonal, 27,159 tilings to k = 13.
Half pentagon, 567 tilings to k = 14. A regular pentagon cannot tile the plane; half of one does, at k = 1, and twice over.
Half hexagon on the edge midpoints, and the domino, one tiling each.
The family is exactly six boards, and that is settled rather than merely unexplored: the angles force the side count to divide 8, and an edge-parity count empties everything else.
393,527 spherical on 10 boards, 91,410 hyperbolic on 10 boards.
33,800 more hyperbolic polygon patterns on 9 boards, and 21,642 on a new Schwarz board.
Fixed
Curved tiles with a deeply bowed edge draw correctly. Bending one far enough cut a notch the old triangulation could not see, and it painted outside the tile.
Error pages that draw a tiling
v1.21.015 August 2026feature release
New features
The error and 404 walls open on a real tiling instead of a blank page, with a live pick from the atlas replacing the seeded one as soon as it loads.
Every edge of these tiles lies on a mirror of the tiling, which forces the outline to a regular hexagon, a rhombus, a rectangle, a square or a triangle. What separates the types is the motif inside: six marks per tile on IH19, one on IH48, IH80 and IH87.
Line weight matches the flat view at the same slider setting. Near the rim of the lens it drew 7 pixels of ink where the flat view drew 2, and thinned to hairlines toward the centre.