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The only one I know of is "HEX" where hexagonal tiles are fitted together, but the colours of their edges must match their neighbours.

If the "things" are only 2 dimensional (flat), then you are probably thinking of "tessellations" where regular geometric shapes are placed together to fill a complete area without leaving an empty space; very easily done with triangles, rectangles, hexagon, but not a pentagon (5 sided). Many examples can be seen in tiling patterns. In fact the word "tesserae" means "tiles", and very small pieces of marble or other stones can be laid on the floor of a Roman villa or temple to produce a picture.

If you are talking about 3D shapes fitting together the easiest example is a cube. That's why Oxos fit so well inside their box. Brick walls use rectangular solids (in mathematics "cuboids"). Triangular prisms will fit too. Triangular pyramids have to be carefully designed if they are to fit together with no empty spaces between.

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