1. When there are identical triangles and quadrangles (or combinations of triangles and quadrangles) and regular polygons, only regular triangles, quadrangles and hexagons can be closely arranged.

2. Regular hexagons are densely laid, because each internal angle is 120, and each splicing point can just accommodate three internal angles; Regular pentagons cannot be densely laid, because each internal angle is 108 degrees, and 360 degrees is not an integer multiple of 108, so there is no gap and overlap in the internal angles of each splicing point. Except for regular triangles, regular quadrangles and regular hexagons, other regular polygons are not allowed to closely arrange planes.

Extended data

The benefits of learning graphic dense shop

1. Go through the process of exploring the conditions of polygon dense laying (mosaic) to further develop students' reasonable reasoning ability.

2. In the process of exploration and communication, cultivate students' habit of cooperation with others and the spirit of questioning.

3. In the process of jigsaw puzzle and exploration, cultivate students' problem consciousness and rigorous and scientific attitude.

4. By exploring the dense laying of plane graphics, we can understand the conditions of dense laying of graphics and experience the mathematical thinking methods such as transformation. Mathematical thinking methods such as experience transformation.

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