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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Your ds game?!?
You can build a fort with him, you can color with him, or you could play a game with him [ Connect4, twister, hide and seek, I spy, etc.]
Regular polygon = n-gon which means the shape must have equal points & sides, and all sides must be equal and all angles must be equal. equilateral triangle is technically a regular polygon, and can go up to whatever, the sky's the limit in size and complexity. regular polygons can be used for lots of things useful. Computer programming algorithms and formulas for many things can be derived from shapes, video game programmers must use polygons to model the details in video games, since perfect circles or other shapes are more graphically intense in any 3d game, polygons are used to add detail and efficiency of the graphics, making it undistinguishable to the human eye but in computing terms it is WAY more efficient to use polygons as shapes. Also desigas from houses, to products you buy, even some company logos use shapes or polygons to make or construct their logo image, or branding mark. Graphic designers also use polygons and other mathematical equations for images, smooth vector images (the images that never blur the more you zoom in, that's vector art!! Aka Math,!!! in all, I hope this helped you out, in what I'm assuming is your homework assignment or at least part of it. :-p
Some roleplaying game die and puzzles such as the Rubik's Cube are shaped like tetrahedrons.
It can mean a time when things are getting busier in preparation for a large event. IE Practices are getting tough ramping up for the big game.