# Polyiamond and Polyming Tiling

## Tiling Triangles

 Tiling a Triangle with a Polyiamond. Tile a triangular polyiamond with copies of a given polyiamond. Tiling a Triangle with Two Polyiamonds. Tile a triangular polyiamond with copies of two given polyiamonds. Tiling a Triangle with a Scaled Polyiamond. Tile a triangular polyiamond with copies of a given polyiamond at various scales. Tiling a Triangle with a Scaled Polyming. Arrange scaled copies of a polyming to form a triangle.

## Tiling Pentagons

 Tiling a Pentagon with a Scaled Pentiamond and Hexiamond. Arrange scaled copies of a pentiamond and a hexiamond to form a polygon with 5 sides. Hexiamond Pair Pentagons. Arrange copies of two hexiamonds to form a polygon with 5 sides. Heptiamond Pair Pentagons. Arrange copies of two heptiamonds to form a polygon with 5 sides.

## Tiling Regular Hexagons

 Two-Hexiamond Balanced Hexagons. Tile a regular hexagon with two hexiamonds in equal quantities. Polyiamond Hexagon Tiling. Tile a straight or ragged hexagon with various polyiamonds.

## Convex Shapes

 Minimal Convex Polyiamond Tilings. With copies of a given polyiamond make the smallest convex polyiamond. Convex Polygons from Pairs of Polyiamonds. With copies of two given polyiamonds make the smallest convex polyiamond. Convex Polygons from Pairs of Scaled Polyiamonds. With as few scaled copies of two given polyiamonds as possible, using at least one of each, make a convex polyiamond. Polyiamond Convexification with Holes. Arrange copies of a given polyiamond to form a convex polyiamond with single-cell holes in it. Convexification Numbers for Polyiamonds. Pack copies of a polyiamond into some convex polyiamond, leaving as few cells vacant as possible. Convex Polygons from the 12 Hexiamonds. Arrange the 12 hexiamonds to form a convex polyiamond. Convex Polygons from Three Hexiamonds. With copies of three given hexiamonds make the smallest convex polyiamond. Similar Polyiamonds Forming a Convex Shape. Arrange scaled copies of a polyiamond to make a convex polyiamond. Tiling a Convex Shape with a Polyming. Arrange copies of a polyming to form a minimally convex shape.

## Other Tilings

 Two-Hexiamond Balanced Parallelograms. Tile a parallelogram with two hexiamonds in equal quantities. Polyiamond Tilings With Few Sides. Arrange copies of a polyiamond to form a polygon with as few sides as possible. Full Symmetry from Pairs of Hexiamonds. Use copies of two hexiamonds to form a shape with full (snowflake) symmetry. Hexiamond Triplets. Arrange the 12 hexiamonds to form three congruent polyiamonds. Yin-Yang Diamonds. Arrange the 12 hexiamonds to cover a bi-colored diamond. Tiling a Polyhex with the 12 Hexiamonds. Arrange the 12 hexiamonds to form a polyhex. Similar Hexiamond Figures, 2–2–8. With the 12 hexiamonds, make three similar figures, one at double scale. Polyiamond Bireptiles. Join two copies of a polyiamond, then dissect the result into equal smaller copies of it. Uniform Polyiamond Stacks. Arrange copies of a polyiamond to form a shape with equal, contiguous rows of cells with even length. Containing Pairs of Hexiamonds. Find the smallest polyiamonds that can contain every pair of distinct hexiamonds. Polyiamond Irreptiling. Dissect a polyiamond into smaller copies of itself, not necessarily the same size. Polyming Irreptiling. Dissect a polyming into smaller copies of itself, not necessarily the same size. Scaled Polyiamond Tetrads. Arrange four copies of a polyiamond at varying scales so that each borders the others. Tiling a Shape with Ternary Symmetry with the Heptiamonds and the Tetrahexes. Tile a shape with 3-fold symmetry with all 24 heptiamonds, then with all 7 tetrahexes. The Lobster and the Snake. Four puzzles about the Lobster and Snake hexiamonds.

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Col. George Sicherman [ HOME | MAIL ]