What shapes tessellate perfectly?

Squares, equilateral triangles, and regular hexagons are the only regular polygons that tessellate perfectly (tile a plane with no gaps). Hexagons are the most efficient, enclosing the most area per perimeter.

How do I add gaps between tiles for a grouted look?

Set the gap width to 0.8-1.2mm for a visible grout line effect. For FDM printing, gaps smaller than your nozzle diameter may not print cleanly. A gap of 2x nozzle width gives the cleanest result.

Can I print tessellated panels on a standard printer?

Yes. For panels larger than your build plate, split them into sections and join them. Each section should end at a tile boundary for clean joins. Use alignment pins or dovetails to connect sections.

What is the best tile size for 3D printing?

Tiles between 10-30mm work well on most FDM printers. Smaller tiles show more detail but take longer to print and may lose definition. Larger tiles are faster but may not look as intricate.

3DPrintCalcs

Tessellation Calculator — Tile Dimensions & Counts

Calculate tile dimensions and counts for tessellating surface patterns.

Surface Width

Total width of the area to tile, e.g. your build plate or panel (mm).

Surface Height

Total height/depth of the area to tile (mm). For a single print, keep within your build volume.

Tile Size

Edge-to-edge width of a single tile (mm). 10-30 mm prints well on most FDM machines.

Gap Between Tiles

Grout/expansion gap between tiles (mm). For a clean FDM print keep it at 2x your nozzle width or more; use 0 for a seamless tessellation.

Tile ShapeSquare, hexagon and equilateral triangle are the only regular shapes that tile the plane gap-free; the 60 degree rhombus (two triangles) also tessellates.

How We Calculate This

Tessellation Formulas

Tiles per row = Surface width / (Tile size + Gap)
Tiles per column = Surface height / (Tile height + Gap)
Total tiles = Tiles per row x Tiles per column
Coverage = Total tiles x Tile area / Surface area x 100%

Counts are an estimate based on bounding-box pitch: tiles across uses the horizontal column spacing (for flat-top hexagons that is 3/4 of the tile width), tiles down uses the row height. A true interlocking offset layout can fit roughly one extra row or column, so the count may differ by +/-1 from a nested arrangement. Tile areas use exact geometry: square = side squared, equilateral triangle = (sqrt(3)/4) x side squared, regular hexagon = (3 x sqrt(3)/2) x (side/2) squared, and 60 degree rhombus = side squared x sin(60).

Frequently Asked Questions

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Last updated: February 2026

All calculations are estimates. Always verify settings with test prints before committing to final prints.